When you first log into Challengermode you can find all the available games in the leftside Menu, the games you have an account for will be in Your Games - any game you still need to connect an account for will be under Other Games.
To add a Summoner for League of Legends you can do one of two things.
Either hover your mouse over the game League of Legends in the menu to the left, three dots will appear (...) - click these to open up a sub-menu.
In this menu you will find Add Summoner in the bottom, click here to add a new League of Legends Summoner.
You can also click the game name, League of Legends, in the menu - this will redirect you to the League of Legends game page which will look like as on the example image below.
You can find the Add Summoner button below the game title on this page, it has the same function as the earlier mentioned Add Summoner button.
You then enter the name of your Summoner (the name of the LoL game account) and choose the region.
Europe West (EUW) and Europe North & East (EUNE) are currently supported on Challengermode.
Once your summoner is found you can choose to verify it manually if you want to play in the daily ladder right away.
If not, you can add your Summoner anyway. (Your summoner will be verified automatically if you play a tournament or a challenge using a Tournament Code.)