I too was masters when I made the swap over to leagues, my basic advice is to choose one role and champion to bring you a majority of the way.
Reaching level 30 is a long process, but what's available to you afterwards is worth it.
Dont spend your IP on phase 1 or 2 runes either, buy up to 5 champions, in case your main role is taken and spend the money on rune pages instead of runes. Set up your masteries per role you want to play and remember your arts of war from starcraft, such as patience.
let the enemy make the first mistakes.
last hitting creep can also be more valuable than kills, watch your minions and make your pokes when they are making cs and always remember to ward / map awareness.
At low levels you may find a team that never wants to end a push, this doesnt have to be you.
it's late but when I wake up I may get around to more useful tidbits.
tier 3 runes will be your best friend, and IP is very valuable if spent right early on, you will see yourself climbing ranks quickly with this advice