The info below is from 2015.
Gili Trawangan to Gili Meno
There are 2 public boats: one at 9:30 & the other one at 16:00. It costs 35'000 IDR. It takes around 10 minutes.
There are also some speed boats running every hour. The price is 100'000 IDR. Note that you don't actually need a speed boat, as the islands are super close to each other anyway, I'm not even sure what they mean by speedboat it may just be a way to justify a price that's almost tripled.
Gili Trawangan to Gili Air
There are 2 public boats: one at 9:30 & the other one at 16:00. It costs 40'000 IDR. It takes 20 minutes.
Note that currently it's the same public boat that takes people to Gili Meno first, and then to Gili Air, hence the same departure times.
Speedboats to Gili Air are also 100'000 IDR and also run every hour.
Please find below a photo of the price board from the official ticketing office in the Gili islands.