Ruy Lopez has been my go-to chess opening recently. I have also played it quite a bit as black. Here's the two main ideas in Ruy Lopez and the most common mistakes related to them.
This will probably be interesting for you if you happen to be ~ 1200-1300 elo on Lichess (subtract maybe a hundred elo or something for the corresponding value on chess.com).
After playing the opening moves,
1. e4 e5
2. Nf3 Nc6
3. Bb5 ...
many of my opponents playing white have thought: "Hey, if I trade my light-squared bishop for the knight on c6, blacks e-pawn becomes free to take!" and so they play:
3. Bb5 a6
4. Bxc6 dxc6 (or bxc6)
5. Nxe5 ...
and then they get obliterated by 5. ... Qg5 forking the greedy knight and white's g-pawn or 5. ... Qd4 forking the same knight and white's e-pawn. In the first option white is also in danger to lose their kingside rook if they don't play cautiously.
Please stop making this mistake, I have had too many boring wins because of this. Instead, you should castle first and use your light-squared bishop later on to gain an advantage in the center.
Another important idea in the Ruy Lopez is pinning black's pieces to their king. Here's a game I played recently:
1. e4 e5
2. Nf3 Nc6
3. Bb5 d6
4. O-O Bd7
5. Bxc6 Bxc6
6. Nc3 d5
7. exd5 Bxd5
8. Nxd5 Qxd5
9. Nxe5 Qxe5
10. Re1 1-0
When black played the blunder d5 on move 6 I decided to lure them into getting their queen pinned with my rook. After getting pinned black just resigned. This is an additional reason to castle early as white.
That's the two main ideas in the Ruy Lopez in my experience: taking the black knight at the right time and threatening black with pins.