To create a custom loadout, go to the "Champions" tab, select the champion you'd like to create the loadout for, scroll over to the "Loadouts" tab, and then hit "Create New Loadout."
Loadouts are created and customized using cards. You select the five cards you wish to use, then you can adjust the potency of each card with the + and - sliders. Altogether, a loadout can't be any more than 12 points. So you'll have five points automatically from the cards you chose, then you have seven points you can distribute however you like. The descriptions on the cards will adjust as you move the sliders, so you can see the different effects each one is giving you. It won't let you approve the loadout if you don't have five cards or you have less than 12 points.
Once you're done, hit "Save and Exit" and it will pop.