Judaism was originally a sacrificial religion, whereas three times a day an animal was sacrificed to G-D, this took place in the first and second temples. With the destruction of the second temple at the hands of the Romans, Judaism had no more priests, and instead over time the Rabbinic, synagogue, and prayer system was instituted. In place of the three daily sacrifices, there were thrice-daily prayers, instead of priests, there were Rabbi’s/teachers, and instead of the temple, there were synagogues. This was a massive change within Judaism, that was done out of necessity as Jews were cast into the diaspora around the world.
The three prayer times are Shacharit corresponding to the morning offering, Minhah corresponding to the afternoon offering, Maariv corresponds to an evening offering. Shacharit is the longest prayer sequence, Minah is the shortest and Maariv falls in-between in length. The Amidah is the central prayer in each of the three daily prayer sessions, with the Sh’ma in Shacharit and Maariv sessions.
The two prayers directly commanded in the Torah are the Sh’ma and the Birkat Ha-Mazon (after meal grace), while Birkat Ha-Mazon is spoken after each meal, the Sh’ma is supposed to be recited in the morning and evening. Another prayer recited daily is the Amidah (Hebrew for standing) and while facing Jerusalem (eastward) you recite a series of blessings. The Amidah is comprised of words of praise, petitions, and finally, words of thanks.
I find that coming from a pagan background and having prayers sparsely utilized, that to get me in the habit of thrice-daily prayers, I practiced the Sh’ma first, three times a day, then in time, I added the others piece by piece until it was a natural feeling. Of course, removing the Sh’ma in midday prayers felt unnatural at the time, mainly because it is honestly such a beautiful prayer, you want to recite as much as possible. The Amidah prayer feels less like a static prayer and more like a conversation directly with G-D, I suppose this is the intention of it, as when you deliver the Amidah it feels very much so like a conversation between a master (G_D) and a servant (You).