You kill your enemy laner over and over.
If, god forbid, this doesn't work or stops working, then you run down the river and kill an enemy from one of the other lanes.
Now if you're an extra intelligent assassin, you'll pop a ward into the enemy jungle on the way down or back. At some point someone on the enemy team is going to get greedy and try to farm a camp while low on health, and you walk in for the kill.
If none of the above work out, try to stall the game till the lategame teamfights. Write "splitpush" and "clean-up" on two slips of paper and glue them to each side of a coin. Toss the coin and commit to whatever you get. Because if you don't commit, you're going to have a choice, and if you have a choice, you're going to waste time deciding. Eventually, from your successes and failures, you'll begin to see which works when, and then maybe you won't even need the coin anymore!