Ber- is the affix to start with because it almost never changes shape and its meaning is broad enough to guess.
What it does
It makes a verb that does not take an object. Roughly: to have, to wear, to use, to be in a state, to do together.
berbicara ‘to speak’, from bicara
berjalan ‘to walk’, from jalan ‘road’
bermain ‘to play’, from main
bersama ‘together’, from sama ‘same’
From a noun: having or wearing
This is the productive part, and it lets you build words you were never taught.
bertopi ‘wearing a hat’, from topi
berkeluarga ‘to have a family’, from keluarga
beruang ‘to have money’, from uang
berwarna ‘coloured’, from warna
Dia berkacamata. ‘He wears glasses.’
An English speaker reaches for a verb like “to wear” and then a noun. Indonesian wraps the noun.
The three shape changes
Only three, and they are worth memorising because ber- is everywhere.
Before r, it drops the r: ber + renang → berenang ‘to swim’
Before a root with -er- in the first syllable, same: ber + kerja → bekerja ‘to work’
One irregular: ber + ajar → belajar ‘to study’
Belajar is the only common word doing that, and you already know it.
Ber- against me-
Ber- verbs do not take an object. Me- verbs usually do.
Saya berbicara. ‘I speak, I am speaking.’
Saya mengajar. ‘I teach’, and there is a class being taught.
If a sentence needs a thing being acted on, ber- is usually the wrong prefix.
The trap
Berapa ‘how much’ is not a ber- word. Neither is berat ‘heavy’ or berita ‘news’. The letters happen to line up.
The test: remove ber- and see whether what remains is a real word. Apa is a word, but berapa does not mean “having what”. Ita is not a word at all. When stripping gives you nonsense, the prefix was never there.
What you’ll actually hear
Speech drops ber- constantly on common verbs.
What the book says: Saya berbicara bahasa Indonesia.
What you’ll hear: Aku bisa bahasa Indonesia.