This is an excellent question whose answer is misunderstood by many.
Understanding the foundations upon which it rests leads to a much deeper comprehension of what it truly means to dedicate ones life (מסירת נפש) when saying the word, "One" (אחד) while reciting the first sentence of the Shema (Devarim 6:4).
שְׁמַ֖ע יִשְׂרָאֵ֑ל יְהוָ֥ה אֱלֹהֵ֖ינוּ יְהוָ֥ה ׀ אֶחָֽד׃
From one perspective, just like G-d is one, so too, the Torah is one. That He (הוא) and His will (רצונו היינו רצון העליון) are one and G-d's will is dressed or enclothed in His Commandments which are written in the letters of the written Torah. This is like is taught in Mishnah Avot (Pirkei Avot), 6:10 which says:
חֲמִשָּׁה קִנְיָנִים קָנָה לוֹ הַקָּדוֹשׁ בָּרוּךְ הוּא בְעוֹלָמוֹ, וְאֵלּוּ הֵן, תּוֹרָה קִנְיָן אֶחָד, שָׁמַיִם וָאָרֶץ קִנְיָן אֶחָד, אַבְרָהָם קִנְיָן אֶחָד, יִשְׂרָאֵל קִנְיָן אֶחָד, בֵּית הַמִּקְדָּשׁ קִנְיָן אֶחָד. תּוֹרָה מִנַּיִן, דִּכְתִיב (משלי ח), ה' קָנָנִי רֵאשִׁית דַּרְכּוֹ קֶדֶם מִפְעָלָיו מֵאָז.
Five possessions did the Holy Blessed One, set aside as his own in this world, and these are they:The Torah, one possession; Heaven and earth, another possession; Abraham, another possession; Israel, another possession; The Temple, another possession. 1a) The Torah is one possession. From where do we know this? Since it is written, “The Lord possessed me, Reishit of His Way, prior to His works of old” (Proverbs 8:22).
This last phrase, prior to His works of old, is in keeping with the concept found in Midrash and Kabbalah that the Torah proceeded Creation by 2000 years. It is literally the blueprint from which all of existence comes.
See also the teaching of the Alter Rebbe like is found in the Tanya, Chapter 40:1, and also the Rishon, Rabbi Meir Ibn Gabbai in Avodat HaKodesh 3:23:1 for a more extensive and deeper understanding of this.
And this teaching from Mishnah Avot refers back to the very first word in the first sentence of the written Torah, Bereshit (בראשית).
That although commonly mistranslated as, In the beginning..., Rashi explains that according to the Hebrew grammar, this means, On account of, or for the sake of Reishit... and cannot mean, "In the beginning...". And that this term, Reishit is actually referring to the most choice, first fruits of G-d's produce, which include both the Torah itself and Israel which are both called Reishit. That G-d, His name and His causations are all one.
יהוה אחד ושמו אחד,דארייתא וקדוש ברוך הוא אחד ומי כעמך ישראל גוי אחד בארץ
And yet, we are also taught that there is a Written Torah, the five books of Moshe, and an Oral Torah which is all the teachings found in the entire oral tradition, in Mishnah, Agadah, Halacha and Midrash which comprise the Talmud and all the other Holy books of Jewish tradition.
One could imagine that this Oral Torah was something else, something extraneous and additional to what we have received from G-d directly. But this is contrary to Jewish tradition.
Encoded in the written Torah itself, encoded according to all the many detailed requirements that go into the formation and meanings of the letters and text of the written Torah itself (the laws of Safrut and the details of the Masorites), which in the broader sense are also the grammatical dimension of Hebrew letters and language comprising the text, are concealed the entire oral Torah. This encoding is also called the Parpra'ot, meaning the auxiliaries of Wisdom like in Mishnah Avot 3:18. This means that to comprehend the Wisdom of the Torah, these methods are indispensable.
And this method of encoding was also taught to Moshe Rabbeinu, both while he was in the cloud, receiving the ten commandments at Mount Sinai and also what he was taught in Egypt in the Yeshivah in Goshen from that tradition which had been transmitted to Avraham, Yitzchok and Yaacov and their forebears like Shem, as in Malchizedek and Eiver, Methuselah, Chanoch all the way back to Adam.
Many of these encoding methods are found for example in the introductions to published Talmud today, like the 32 Hermeneutical Rules of Rabbi Eliezer ben Yossi HaGalili and the 13 Middot of Rabbi Yishmael by which the written Torah is explained. Another large part of this encoding method can be found in the remnant of the books which we have today from Rabbi Akiva ben Yosef, The Letters of Rabbi Akiva and also The Crowns of Rabbi Akiva, both of which are mentioned explicitly in the Talmud. These last two are referenced and quoted extensively in later generations by people such as Ramban and the Tur in their commentaries to the written Torah, or in the sefer Halacha called Sefer Ohr Zaruah.
In this context, it is also worth noting that what we have today of the entire oral Torah is reported to have come to us solely through the teachings of Rabbi Akiva via his five surviving students.
Other early sources which contain other details of this encoding method are, for example, Sefer Yetzirah, a book also mention in Talmud and attributed to Avraham Avinu, Sefer Ma'ayan HaChochma, a book attributed to Moshe Rabbeinu dealing with many of these methods, and Sefer Raziel HaMalach, a book given by the Angel, Raziel to Adam HaRishon after the sin of the tree of Knowledge of Good and its opposite.
In a general sense, this idea of how the Oral Torah is encoded and dressed within the Written Torah follows the concept of Klal and Prat hinted at in the names of the final two parshiyot of the book of Shemot, VaYakhel, which has a connotation of wholeness (the Congregation) and Pekudei, which has a connotation of enumeration. These parshiyot deal with the construction of the Tabernacle where G-d's presence is revealed. And in a similar sense, the book of Bereshit and in particular the first Parsha are paradigms from which the balance of the Written Torah evolve from. And the essence of the whole five books of the Written Torah are likewise encoded and contained within the words and letters of the ten Commandments which in turn are encoded the first commandment and the first word of that commandment (אנכי).
You also ask if these methods can bring you to interpretations that you could not reach by reading at face value? If this part of your question is understood correctly, you mean can these the encoding methods lead to divergent understanding that is in conflict with and contrary to G-d's will?
The answer is yes. The general rule for this is that we are told to conform with whatever is required by halacha, which is generally understood to be the plain sense of the text. But a more nuanced way of understanding this is that the halacha relates to how we connect to physical reality, the universe in which we live. We are to be involved with the real, physical world, reality and truth.
In the language of theoretical physics, those interpretations which seem to depart from the confines or boundaries of halacha are like alternate universes. In the nomenclature of Kabbalah and Chassidut this is often called the Sitra Achra, the Other Side, which is contrary to Torah, meaning G-d's Will and is associated with and leads to the opposite of life. Like it is written in BaMidbar 14:28,
I am life, says G-d!