When a user logins I get him/her\'s ID and save it in a session var. What I wonder is, is this the way to go? Or should I use cookies? so it automatically login and so on.
Yes, this is the way to go. The session itself is already backed by a cookie to remove you any programming efforts around that. The session (actually, the cookie) will live as long as the user has the browser instance open or until the session times out at the server side because the user didn't visit the site for a certain time (usually around 30 minutes).
On login, just put the obtained User in the $_SESSION. On every request on the restricted pages you just check if the logged-in User is available in the $_SESSION and handle the request accordingly, i.e. continue with it or redirect to a login or error page. On logout, just remove the User from the $_SESSION.
If you want to add a Remember me on this computer option, then you'll need to add another cookie yourself which lives longer than the session. You only need to ensure that you generate a long, unique and hard-to-guess value for the cookie, otherwise it's too easy to hack. Look how PHP did it by checking the cookie with the name phpsessionid in your webbrowser.