Once your Fantasy League of Legends group has completed drafting, you'll be able to view your matchup for Week 1.
You can make your pick and ban selections, but your matchup will not begin until the actual League of Legends split begins. Your team earns points based on how will the actual players do, so you're not able to begin your matchup at a specific time.
All matchups will begin automatically as players start accumulating stats. You'll see the points appear as they happen, and you'll be able to see your totals start increasing in the matchup.