Quick answer
Three questions, three sets of answers: где? (where at), куда́? (where to), отку́да? (where from).
The full grid
| где? — at | куда́? — to | отку́да? — from | |
|---|---|---|---|
| here | здесь / тут | сюда́ | отсю́да |
| there | там | туда́ | отту́да |
| home | до́ма | домо́й | из до́ма |
| everywhere | везде́ | всю́ду | отовсю́ду |
| nowhere | нигде́ | никуда́ | ниотку́да |
The three home forms are the ones you will use daily: Я до́ма (I’m at home), Я иду́ домо́й (I’m going home), and neither is в дом or в до́ме.
здесь or тут?
Practically the same. Тут is shorter, more colloquial and more frequent in speech; здесь is slightly more neutral and the one to use in writing. Both answer где?, and the “to here” form for both is сюда́.
The same logic in the cases
This is the в + prepositional versus в + accusative distinction in adverb form. Я в Москве́ / Я в Москву́ is exactly там / туда́. Learning the adverbs first makes the case rule click, because the difference is audible in a single syllable.
Куда́ ты?
A complete, very common question with no verb at all: Куда́ ты? — where are you off to? The куда́ already carries the motion, so идёшь can be dropped.
Typical mistakes
Иди́ здесь!
Иди́ сюда́!
Motion towards needs сюда́.
Я иду́ до́ма.
Я иду́ домо́й.
домо́й is the “to home” form.
Check yourself
Иди́ ___! — Come here!