What would you like to know about the weather in Indonesia?
Indonesia's climate is monsoonal and is affected by a series of weather patterns depending on where you are in the archipelago. Broadly speaking, unless you're hiking the glacier in Papua the weather is hot and wet or hot and dry. Indonesia has no shortage of volcanoes and at higher altitude -- such as when you are climbing them! -- the temperature will drop, but you're essentially straddling the equator and it is warm to hot year round.
As with other monsoonal climates, wet season is characterised by short, heavy downpours rather than all-day, never-ending rain (though the latter does happen). Flooding in parts of most cities in peak wet season is to be expected. Wet season brings with it rough seas and boat timetables (and safety) may be affected.
Generally speaking, Indonesia's wet season is between late October and April/May and the dry season is between April/May and September/October, with the "coolest" period falling in July through August (cool is a relative term in Indonesia). The country is affected by two primary monsoon systems -- the southeast monsoon from June to September and the northwest monsoon from December to March.
The exception to the above is Maluku and Papua, which both have an inverted wet season to the rest of the country, meaning it is dry in Maluku and Papua October through to April or May and wet for May/June through to Octoberish.
There is some seasonal variation year to year. For example, by early December 2015 heavy rains had hit Sumatra and Java, but Bali, Lombok and Sumbawa were dry as a bell -- and officially in drought.
Unless you are planning on spending prolonged periods atop a volcano, you will not need to pack winter woollies for your time in Indonesia.
Indonesia's peak tourism season coincides with the middle of the dry season and European summer. A second, lesser peak season stretches across the middle of the monsoon season in December and January when, in particular, Australians flock to the country for their summer holidays.
When to visit depends somewhat on your interests. If you plan to climb volcanoes, dry season is better, with some peaks being closed to trekking at the height of the wet season. If you're a surfer, much will depend on where you are planning on surfing. If you're after a more typical holiday break, we'd suggest the shoulder of the dry season -- to get the best of the weather before half of France and Italy arrive (or after they've left).
If you're planning on visiting in wet season, be prepared for a lot of waste in the water and some seriously filthy beaches. Indonesia is under (a largely self-inflicted) siege by waste, and while we imagine "surf Kuta in a sea of used nappies" probably isn't a slogan the tourism department would be fond of, it isn't far off the truth.