I have a logging in problem in League of Legends

There was an error logging into the game. Please try again. If the issue persists, please visit the League of Legends website for updates

what should I do now?

First off, check League of Legends' Service Status, it's their official page, and whenever there's a problem with the server, it's listed there (Note that depending on your region you may have to click on the box to the right and select your region.

If everything's alright there, then it's on your end. As such, try to restart the client (close everything, including with Task Manager just to be sure). Then launch the client (In Administration mode).

If that still doesn't work, then check your Firewall/Anti-Virus settings. The Firewall may have blocked it, or a virus may have disabled some of your connections.

If after all of that it still doesn't work, then shutdown your computer. It's unlikely that you get to this stage, but just manually reboot the PC in order to make sure it isn't a Runtime problem. It should be fixed by now.