To design a good new game you need to be familiar with a variety of existing games. You should get in the habit of thinking about a game while you play it, to try to understand what the designers of the game were thinking. Much like analysing a novel in English class there are many different ways to do this, so I have made a list of questions to think about while playing. You could write the answers down afterwards.

Modern games can be quite complicated, so it’s easier to start with older games. To play these you will need:

An emulator. I recommend Ludo because it emulates many different old systems.
A ROM file for each game you want to play. (Downloading ROMs may be a breach of copyright law, although it may not be if you own the game, are doing it for educational purposes, or if you download from the Internet Archive which has an exception from copyright law. Check with a lawyer who specializes in international intellectual property laws .)

Questions

Title
Year
Publisher
System
What genre(s) is the game?
What are the controls?
What style is the artwork?
What sort of music and sound effects does the game have?
What is the objective of the game?
What stops you from completing the objective?
What skills are needed to be good at the game?
What do you like about the game and why?
What don’t you like?
What would you change?
How are other (newer) games similar and different from this game?