I am starting to study openings, and I have a question. When you start with a move in an opening, say Ruy Lopez. And you make the first move, when your opponent doesn't follow the move for black, does it then become a variation of that opening? And if so what and how many variations of that opening do I study? I am very curious on how to proceed to begin my study.

Well, I think if your opp doesn't follow your move in an opening line it can become another opening or the variation of that opening. Example : the Ruy Lopez is 1. e4 e5 2.Nf3 Nc6 3. Bb5, but if your opponent play 2. ... Nf6, it becomes the petrov defense. But in Sicilian defence 1.e4 c5 2. Nf3, here either your opponent play 2. ... Nc6 or 2. ... d6 or 2. ... e6 it still is the Sicilian Defence, but in its other 's variation.

I think, the first thing you must do is not learning of the variation of some openings, but to learn the basic principle of the opening :

1. Develop your pieces towards the center
2. Develop Knights before bishops
3. Castle early
4. Don't bring your Queen out too early
5. Gain more space than your opponent
6. Develop while preventing your opponent to develop his pieces, etc.
   

And remember the objective of opening is to develop your pieces and gain control of the center. I think Ruy Lopez and Italy is a good opening to implement the opening principle, if your opp doesn't play like the opening line, just remember the opening principle. After that you can try some opening and choose which opening suit your style of play best. 

And you make the first move, when your opponent doesn't follow the move for black, does it then become a variation of that opening?

It might be a variation of your opening or another opening entirely.

And if so what and how many variations of that opening do I study? 

I wouldn't study any variations. Upto the 1200 level, mastering general opening principles is the most important thing. By the 1600 level you should know the mainlines well and be able to explain key themes and ideas.

The reasons for not learning variations at the <1200 level is two-fold: (a) your opponents are going to leave book early on, so your preparation will be nearly worthless, (b) when your opponent 'goofs' you will only gain a tiny edge like a single tempo--you can't capitalize on such minor gains until you're past the stage where you miss tactics.

Another way to do it, is after you play a game where your opponent deviates from the mainline, lookup and learn that variation. That tends to be a more profitable form of study than memorizing lines that have never been played against you. :)

Thanks and good luck BTW!!!