The simplest way to get your laundry done in Indonesia will be asking your hotel. However, often they will charge a fairly steep premium.
Higher end hotels in Indonesia sometimes offer free pressing for a set number of pieces per day. Some also offer free laundry for a set number of pieces per day.
A cheaper alternative is to use a local laundry, which also often can arrange dry cleaning. They usually charge by the kilogram and may charge a premium for express service. You can ask your hotel where the nearest laundry is, alternatively look around or ask. Most will be signed, and some have the clear look of a laundry shop (steam coming out), piles of laundry in the window and so on). You could also try a search on something like Google Maps though in Bandung at least I didn’t find it much use in locating laundries. Instead, walking down the road, I spotted “Clean Fresh” (Jl. Lengkong Besar No. 20, Bandung) which sounded like and indeed was a laundry. For rush service, one kilo was IDR30,000 (twice the standard price) and ready in a couple of hours. For an extra IDR15,000, they put it on a motorbike and dropped it off at my hotel a mile away. For comparison, the hotel charged me IDR20,000 to wash and press one shirt.
As in other southeast Asian nations, the laundry will often come wrapped in plastic. If each piece is like this it can be a bit cumbersome to remove, so you may try to explain that you do not want it.
Self-service launderettes mostly do not exist in Indonesia, and may not offer much cost advantage over sending out to a laundry. But in tourist centres like Bali there are a few.