I am studying to convert to Judaism and one of the questions I was asked was about the Ten Commandments. I remember reading at that time that there was debate about the division of the statements Moses brought down on tablets and that they are, in Hebrew, more commonly called the "Ten Statements" than the "Ten Commandments." I am particularly interested in the "first" and whether or not it is considered a commandment to believe in G-d. After all, how can a person be commanded to have a particular belief?
Belief in God cannot possibly be a commandment.
A commandment is something one fulfills because he already believes in the one who is commanding it. Thus, a commandment to believe in the existence of the commander is an absurdity; it assumes in its fulfillment that it has already been fulfilled. (This argument was presented by R' Hasdai Crescas.)
For this reason, many Rishonim did not count those first few words of the ten statements - "I am the LORD thy God, who brought thee out of the land of Egypt, out of the house of bondage" - as a commandment, but rather as an introductory line to the entire monologue. [There is a Talmudic statement, though, that the first two commandments came from God directly, and they are identified as the first two statements of the ten. How to count those two commandments is a discussion in itself.]
Now, what to make of the Rambam, who counted belief in God as the first commandment, and tied it to this first verse of the ten commandments? The answer is proposed by Abarbanel in Rosh Amanah as follows:
The commandment is not belief in God, but rather the belief that God has certain qualities, namely that He is independent of all other existences and that all other existences are dependent upon Him. This is evident from Rambam's description of this mitzva in the Mishna Torah (Hil. Yesodei Hatorah 1:1-3) (my own translation):
A more detailed description of this idea can be found in the first of Rambam's thirteen principles. Essentially, the commandment is that we should believe that God, whom it is already assumed that we believe in His existence, possesses the above qualities.
What about the fact that I cannot command someone to believe something? A person believes what he believes; he cannot be forced. To this Abarbanel responds that the commandment is not to actually believe, but rather to contemplate. We are commanded not to blindly follow faith, but rather to strive toward knowledge and to weigh it approprately to come to the conclusion that the above is true. (Admittedly, I don't fully understand this concept, but it seems that given the information that is available to us and our traditions, it is reasonable that we come to the correct conclusion.)
See this article for more information.
There is no question that knowing that Gd exists is a Commandment (Mitzvah). It is listed as Mitzvah number 1 in Rambam's list of 613.
However, in Judaism we have an obligation to Know, and to learn, and to understand that Gd exists, not to believe, in the Western understanding of the word believe.
As you state in your question, how can you force a person to believe something they don't, or how can you even ask them to? It's impossible!
The Hebrew word for "faith" or "believe" is Emuna. And there is certainly a mitzvah to have Emuna IN hashem, in addition to the mitzvah to know and understand that Gd exists. The main difference here, is that in modern western colloquial speech we talk about "Faith THAT Gd Exist", instead of "Faith IN Gd". The difference is large. One does not need Faith that a parent exists. However, if a parent is abusive or doesn't follow up on their word, a child might lose faith in that parent. The same meaning here is for Gd. We must trust that Hashem will provide for us, that He will keep his word, etc.
The first commandment of the 10 commandments is that we should know and understand and have faith that Hashem, the creator of the World, is the same Gd that took us out of Egypt and deals kindly with the Jewish people. We must build a relationship, learn about Gd's ways, and have faith In him.
There are different views among the rishonim whether this belief counts as one of the 613 mitzvos or is a more fundamental basis for all Judaism. Either way, it is definitely obligatory, and without the belief in God, Judaism is meaningless.
Just as God commanded man to not believe in other gods, He also commanded us to believe in God. Someone who believes in a rain-god must work at eradicating this belief, perhaps by recognizing that the clouds and rain are not an interdependent force, but part of nature. Similarly, if one doesn't believe in God, he should work at recognizing God. For example, by recognizing that there has to be a source of the world's existence, or that the universe is too fine-tuned to have happened by chance.
There are two parts to your question.
The first is an apparently simple question as to whether or not there is an actual commandment in Judaism to believe in God. Maimonides, and most other authorities, consider the obligation to believe in God to be one of the 613 commandments, and see this as the commandment expressed in the first sentence of the 10 "commandments". There are some authorities, such as the Behag, who did not include this obligation in their catalog of the 613 commandments.
It is important to understand that all of these opinions, whether or not they include the obligation to believe in God in their formal catalog of the commandments or not, consider belief in God to be absolutely obligatory and foundational to Judaism. There are several reasons why the belief in God might not be listed in a formal catalog of the commandments. One simple reason is that the concept of a commandment presupposes the existence of an authority that issues commands. A commandment to believe in the existence of the authority that issued the commandment is logically impossible. In this sense, belief in God would constitute a kind of "meta-obligation" that exists independently of, and logically prior to, the commandments.
This question is so basic that it raises the question of how to understand the position of those, like Maimonides, who included the obligation to believe in their catalog of the commandments.
It also brings us to the second part of your question, how can a person be commanded to believe in God? Either he believes, in which case the commandment is unnecessary, or he doesn't believe, in which the commandment has no authority to him.
(I would point out that this question does not apply to other beliefs. Once a person has accepted that God exists, and that He reveals His will to human beings, then it is perfectly possible for Him to command us to believe various other things, which we can and must believe based only on the authority of His statement.)
There are several answers to this question, all of which basically create a separation between the basic recognition of God's existence, which, in fact, cannot be commanded, and the commandment of belief, which starts only after that basic recognition has been achieved.
One such approach is that the commandment to believe is to internalize that basic intellectual recognition of God's existence into our personality. There is a great distance between intellectually acknowledging a truth and making that truth an integral part of how you think and feel. There are a wide range of methods that can be used for this purpose. It is this that we are commanded to do by the first commandment.
A somewhat different, more mussar oriented, approach is found in other sources (the best known exposition of this approach is from Rabbi Elchonon Wasserman). This approach argues that the truth of God's existence is so self-evident that it should be immediately obvious to any person of normal intelligence. Why then do so many intelligent people fail to recognize this truth? The answer is that human beings have an extraordinary talent for self-deception, and when we don't want to accept a truth, we are very capable of fooling ourselves into believing that the truth isn't true.
According to this approach, the commandment to believe is a commandment to work on ourselves to remove those natural inclinations and character flaws that cause us to fool ourselves and to deny that which should be obvious. Once we do so, the truth of God's existence will come naturally as a self-evident truth.
Based heavily on this answer of mine
The answer to this question is classically understood to be subject to a debate between the Rambam and the Behag. The Rambam did count belief in God as one of (in fact, the first of) the 613 commandments, and proves that it should be counted as such due to a Talmudic comment on the first of the 10 Commandments. However, the Behag (who preceded the Rambam) doesn't count this as one of the commandments.
R. Chisdai Crescas, R. Yosef Albo, Abarbanel, and so many others ask a fundamntal question on the Rambam, who counts this as a mitzvah. They ask, how can one command someone to believe? First of all, it's useless, because either someone already believes in God, and if he doesn't, a 'mitzvah' to do so won't help. Additionally, it doesn't make sense to have a mitzvah for something that is outside of one's control; these rishonim thought that a person can't just will himself to believe that something is true if he already believes it to be false (though this is a matter of debate in contemporary epistemology).
In order to address this question, some have explained that when the Rambam writes that the mitzvah is to 'believe', he is actually referring to something other than mere 'belief'. Thus, the Malbim (Shemos 20:2), Maharam Schik (Mitzvah 26), Abarbanel (Rosh Amanah ch. 17) and Seforno (beginning of Ohr Amim) all explain that the commandment of אנכי ה' אלוקיך, which we've understood to require believing in God, is actually a command to justify those beliefs, either philosophically or otherwise. (The Rambam himself discusses this in Moreh Nevuchim, specifically 1:50 where he states that in order to fulfill the mitzvah one has to be absolutely certain that God's existence is true, even though one does not have to be able to prove it to not be considered a beretic). If this is not be counted as a mitzvah, perhaps there would be no requirement to justify one's belief, and can be left simply as 'belief'.
Shut Shoel U'Meishiv (Tinyana 1:51, "l'maskil echad") takes the opposite position. He also asks if there's a practical difference between the Rambam and Behag in this regard, and concludes that while according to the Behag, one can come to belief in God through philosophical justification or the like, the Rambam holds that one must belief because it is a mitzvah to do so, and no other reason. (!)
Alternatively, because it's unreasonable to think that there's a command to simply 'believe that God exists', the commandment is to believe that the One God is He Who revealed Himself to our forefathers at Sinai and gave them the Torah. (See Semak Aseh 1, Sefer HaIkkarim 1:14, Drashos Haran no. 9).
A fourth approach is to say that 'belief in God' is primary a command to accept God's sovereignty over oneself. Such a command would actually be a practical matter, as a person who cognitively believes in God may not actually act as if he accepts the consequences of this belief. This is indicated by the comments of the Ramban to Sefer Hamitzvos, lo saaseh 5, and I believe that there are other indications towards this understanding as well.
Finally, the position of R. Elchanan Wasserman (Kovetz Maamarim 1) is that the mitzvah as counted by the Rambam is not referring to an intellectual belief so much as it is a command to be reasonable not to be 'bribed' by the temptations that would be associated with denying God's existence. (I find this difficult for many reasons, though, and I'd love for someone to explain it to me).