This howto assumes that you have the program screen installed on your target system (most will have it).
The first step is creating a new screen-session via
screen -S SomeTellingName
This will open a new session besides your current login shell. There you can start the process(es) which you want to be able to check back after you log in the next time.
To leave the screen-session, press Ctrl-a d. This will detach the session and return you to the login shell. The screen-session will continue running in the background along with the process(es) started inside it.
To re-enter the session use
screen -r TheNameUsedBefore
and you’re there.