if you do that; having done that; in that case
A conditional or sequential phrase meaning 'if/when one does that' or 'having done that'. It connects an action to its result or next step.
If you do that, the problem might be solved.
Press the button. Then the screen will change.
すると is a shorter, more narrative connector meaning 'then/whereupon', while そうすると explicitly refers back to a previously mentioned action.
そうなると focuses on a situation naturally becoming that way, while そうすると focuses on the result of an action being taken.
こうすると points to an action the speaker is doing or about to demonstrate right here, while そうすると refers back to an action already mentioned by someone else or further away.
Compound of そう (so, like that) + すると (when one does, if one does).