At the moment there are two fast boat companies operating from Amed to the Gili Islands.
In high season (from June to October) they run twice a day, in the morning and in the afternoon. During the rest of the year, they only run once a day in the morning.
The price for a one way ticket is around 250.000 IDR (around 18€). You can buy tickets from your hotel. The price always includes a pickup from your hotel to the harbour.
The boats will leave from Amed and make stops in Gili Trawangan, Gili Meno and Lombok before heading back to Amed.