Conversion to Judaism is a major life change, therefore it is much, much more difficult to convert to Judaism than it is to convert to other religions. You must examine your motives for conversion before actually pursuing it. Why do you want to be Jewish? Do you want to become closer to G-d? Unlike other religions, Judaism does not teach that in order to please G-d you must be Jewish. Non-Jews can serve G-d just as well as any born Jew can, by observing the Seven Noahide Laws and living a righteous life.
I would recommend speaking to your local Orthodox rabbi and talking with him about your interest in conversion. He can either help you himself or put you in the right direction.
It is important to note that conversion to Reform or Conservative Judaism does not make you Jewish according to traditional Jewish law. In order to be accepted by everyone as a true Jewish convert, you must go through an Orthodox conversion. Do not settle for anything less.
Ethnicity is not something that has ever been focused on in Judaism, and historically most Jews I have ever known in my life (myself included) have not been racist. But as with any group of people, you will most certainly find people who will be concerned with this. But understand they do not represent Judaism's thoughts on race and ethnicity at all. Besides, Jewish people come in all sorts of colors - there are Jews all over the racial spectrum.
Hatzlachah rabbah (good luck) in your journey!