There are many ways how to keep a process running after logging out. Each if them has its own advantages and disadvantages: nohup, disown, screen, tmux, ssh2go, etc. Here's how it works with screen:
ssh user@server.com # connect to server
screen # start screen
run-a-long-process # start process
CTRL+a,d # to detach from your screen session
exit # disconnect from the server
ssh user@server.com # reconnect
screen -r # resume the screen session