Standard DOSBox does not support savestates. For that, you need a different build, such as DOSBox-X.

And how do you use save in DOSBox-X?

It's not terribly convenient, but GTA 1 does allow saving the game between "levels" -- to end a level you must acquire a certain amount of money or meet some other objective.

And other games?

To answer as vaguely as your question: other games may have similar methods, or different methods, or no methods at all.

whiteportal27 wrote on 2021-06-22, 19:12:

And how do you use save in DOSBox-X?

I assume the process is similar to save states in console emulators. Have you considered reading the documentation?

ripsaw8080 wrote on 2021-06-22, 19:19:

to end a level you must acquire a certain amount of money or meet some other objective.

True, but alas, that can take hours. There was much frustration about that twenty years ago. (I'm a little surprised no one has tried to come up with a practical mod in the meantime.)