Do, can, become, change
The structural action verbs — do (suru, casual yaru), can do (dekiru) and become (naru) — that turn nouns and adjectives into events, plus kawaru for something changing on its own.
suru
polite shimasudo; make
する します
The all-purpose 'do' and the hinge of every noun+suru verb (benkyou suru, shinpai suru), while X ni suru / -ku suru means 'go with X' or 'make it X'.
ima nani shiteru?
What are you up to right now?
今何してる?
ima nani o shitemasu ka?
What are you doing right now?
今何をしてますか?
Irregular: shite, shita, shinai, shiyou.
Learn alongside: yaru
yaru
polite yarimasudo (casual)
やる やります
Casual-leaning 'do' for activities, hobbies, sports and tasks (yatta!, gitaa yatteru, nani yatteru?); yarimasu is normal in everyday polite talk (watashi ga yarimasu), with shimasu the safer choice in formal settings.
nanka supootsu yatteru?
Do you play any sports?
なんかスポーツやってる?
nanika supootsu o yattemasu ka?
Do you play any sports?
何かスポーツをやってますか?
yatta! = 'Yay!' for any good news, not only your own success; yaru also means give to pets and plants (mizu yatta?), and -te yaru (doing for someone) sounds rough.
dekiru
polite dekimasucan do; be ready; come into being
できる できます
The 'can' for skills and every noun+suru verb (unten dekiru, nihongo dekiru), with the skill marked by ga; dekita means 'it's ready / done' and also that something new appeared (atarashii mise ga dekita, kareshi dekita?).
kuruma no unten dekiru?
Can you drive?
車の運転できる?
kuruma no unten wa dekimasu ka?
Are you able to drive?
車の運転はできますか?
Only nouns and suru-verbs take dekiru (unten dekiru, never *unten sureru); every other verb uses its potential form: ikeru, taberareru, never *iku dekiru.
Learn first: suru
naru
polite narimasubecome; turn into
なる なります
Any change of state, as adjective -ku naru or noun / na-adjective ni naru (samuku natta, genki ni natta), and dou natta? asks how something turned out.
samuku natta ne.
It's gotten cold, huh.
寒くなったね。
samuku narimashita ne.
It's gotten cold, hasn't it.
寒くなりましたね。
Past natta reports the new state: samuku natta = it's cold now.
kawaru
polite kawarimasuchange (by itself)
変わる かわる 変わります
Says something changed on its own (a person, plan, place or price), with the thing marked by ga; changing it yourself is the transitive kaeru (kaeta).
kawattenai ne.
You haven't changed.
変わってないね。
kawattemasen ne.
You haven't changed.
変わってませんね。
kawatteru / kawatta often means odd or unusual, not 'is changing' (kawatteru ne = you're a bit unusual; kawatta hito = an odd person). 代わる shares the sound: kawarou ka? = want me to take over?
Learn first: -teru