General Question on Openings

As a newcomer to the serious study of Chess, I am trying to practice openings, but there is something about them I don't understand.  If a specific opening depends on your opponents moving their pieces to certain squares, but they don't, can you still use the opening?

As an example I'll use the Queen's Gambit. (1. d4 d5 2. c4)

Lets say black doesn't move its pawn as shown in the diagram.  But instead, moves a knight out or something.  Is it still a Queen's Gambit?  Does white have to change their opening or strategy?

I'm practicing against the AI a lot, so maybe that's not a good way to practice openings perhaps?  I would appreciate if someone could clear up this matter for me, thx.

When the opponent plays other moves it turns either into a different opening or a different variant of the opening.

If you play d4 and the opponent plays Nf6 then the opponent is likely going to follow some form of Indian attack (King's Indian, Nimzo Indian, etc) or  a Benoni.

If after d4 the opponent plays f5 he's going for a Dutch defense.

The theory for each opening is different so you can't use all of the opening theory from your Queen's Gambit. Like the poster above said you can still play c4 next for just about any response, but from then on the lines will head different ways.

Even in a Queen's Gambit you can have very different opening lines depending on your and your opponents approach. Accepted and Declined for starters.

I think a good way to explore new openings is to play a game and when you get to a position you haven't seen before/don't remember/etc. you play the best move you see and after the game you look into what is typically played there and why.

for your example, moving a knight immediately would be bad:

2. ..Nf6 3. cxd5 Nxd5 4. e4 and white gains the center while kicking the knight.

2. ..Nc6 just blocks the c pawn, which is a must for a solid game by black. Since being solid is the main goal by my opinion c6 is best to fllow up with. 

You can make your opening moves in any order but you should end up with very similar or same positions by the middle game. Otherwise, you will be playing originally and out of theory and will most likely hae a bad position.

Ok, I think I get it now

2...Nc6 is very bad. So bad, that a 2700+ rated super Grandmaster wrote a whole book about it.

2...Nf6 on the other hand is a secondrate move, but certainly not because of the move 4.e4?! which gives Black a rather easy game.

To get to the heart of teh question:

Most openings require the specific moves from both sides of the board. If you want to play a Ruy Lopez and your opponent never plays e5, then whatever it is you're playing, it's not a Ruy Lopez. Similarly with the Queens' Gambit complex, you can make the same moves for white but it ceases to be a Queen's Gambit if your opponent plays 1. ... a6, 2. ... h6, 3. ... Nc6 and never plays d5.

While the opening requires moves on both sides of the board, many openings allow for transpositions and move order nuances that mean multiple opening move orders converge to the same named opening. So, for example something like:

1. Nf3 Nf6, 2. c4 e6, 3. e3 d5 4. d4 ... Is still a Queen's Gambit line even though the move d4 didn't happen until move 4 and the c-pawn was never offered as a gambit pawn.

(note, I'm not saying the above is an example of a good move order by either player).