There are two ways in, and they are not equivalent
You can reach the Gilis from Bali by fast boat across the strait, or from Lombok itself via the harbour at Bangsal on the north-west coast. Most visitors do the first because they landed in Denpasar. The second is shorter, cheaper and much less discussed.
If you fly into Lombok International in the south instead, you never touch Bali at all — you cross the island by road to Bangsal and take a local boat. Whether that is better depends entirely on where your flight lands.
The three Bali ports
Fast boats leave from Padangbai in the east, Serangan in the south, and Amed in the north-east. They are not interchangeable, and the right one is decided by where you are staying in Bali rather than by the boat.
Padangbai is the standard choice and has the most departures; it suits anyone coming from Ubud, Sidemen or Candidasa. Serangan suits south Bali and is close to the airport, but note that some operators sail Serangan to Padangbai first and then on to the islands, which makes the day considerably longer than the headline crossing time. Amed is the shortest sea leg but has the fewest departures, mostly in the morning.
One thing to verify rather than trust: port status and schedules change, and at least one operator has reported Amed closed for construction. Confirm on the operator’s own site for your date before you build a plan around a particular port.
Bangsal, the Lombok side
Bangsal in Pemenang village is the public harbour for all three Gilis and the closest mainland point to them. Public boats run through the day and leave when they have enough passengers rather than to a timetable; local fast boats and private charters also work the route.
Bangsal has a long-standing reputation for touts, and the standard advice from people who use it regularly is the same every time: buy at the official counter or online, and ignore anyone who approaches you before you reach it.
Which island the boat reaches first
Fast boats from Bali generally call at Gili Trawangan before Gili Air, and Gili Meno is the least-served of the three. If you are staying on Meno, expect the last leg to involve either a local boat or a transfer arranged by your hotel — several of the properties on the Meno page list airport pick-up or drop-off, which is worth asking about at the time you book rather than on arrival.
What to check before you pay
Three things move often enough to be worth confirming on the day you book: which port your operator actually departs from, whether the crossing is direct or calls somewhere first, and which of the three islands the ticket drops you at. All three have caught people out, and none of them is expensive to check.
This page deliberately does not quote crossing times, fares or departure times. They change too often for a page like this to be right, and a wrong number here is worse than no number.