to, at, and from

One of the tricky parts of Russian for English speakers is that there are several different words that correspond to the idea of "to," several that correspond to the idea of "at," and several that correspond to the idea of "from." It gets even worse when you try to deal with "for." This page discusses the generalities of to-at-from.

The default phrase for describing motion "to" a place in Russian uses the preposition в followed by the accusative case.

Иван пошёл в магазин. Ivan has gone to the store.

There is a subset of words in Russian that use phrases with the preposition на followed by the accusative case. You can find a partial listing of those words here. Some are just quirky and have to be memorized (почта), and some fall into broad categories like wide flat places (остров, полуостров), or bodies of water (море, озеро), or things you attend (урок, занятие, семинар).

Иван пошёл на почту. Ivan has gone to the post office.

Finally, if you go to a person's place, then the phrase to use is к followed by the dative case.

Иван пошёл к Тане. Ivan has gone to Tanya's place.

For each of these motion phrases there is a corresponding location phrase. For instance if you go to a place using в + accusative, then the corresponding "at" phrase is в + prepositional.

Иван пошёл в магазин. Ivan has gone to the store.
Иван был в магазине. Ivan was at the store.

If you go to a place using на + accusative, then the corresponding "at" phrase is на + prepositional.

Иван пошёл на почту. Ivan has gone to the post office.
Иван был на почте. Ivan was at the post office.

If you go to a place using к + dative, then the corresponding "at" phrase is у + genitive.

Иван пошёл к Тане. Ivan has gone to Tanya's place.
Иван был у Тани. Ivan was at Tanya's place.

Similarly there are unique phrases for coming "from" those places. Here is a chart that summarizes those ideas.

If you go "to" a place using… then you'll be "at" that place using… and you'll return "from" that place using…
в + acc в + pre из + gen
на + acc на + pre с + gen
к + dat у + gen от + gen

Examples:

Иван только что пришёл из магазина. Ivan has just come from the store.
Иван только что пришёл с почты. Ivan has just come from the post office.
Иван только что пришёл от Тани. Ivan has just come from Tanya's place.

Special adverbs and phrases for "to, from and at"

If you go "to" a place using… then you'll be "at" that place using… and you'll return "from" that place using…
here сюда́ здесь, тут отсю́да
there туда́ там отту́да
home домо́й до́ма из до́ма
right напра́во, впра́во напра́во, спра́ва спра́ва
left нале́во, вле́во нале́во, сле́ва сле́ва
down вниз внизу́ сни́зу
up наве́рх, вверх наверху́, вверху́ све́рху
forward вперёд впереди́, спе́реди спе́реди

Examples:

Идите сюда! Come here!
Почему вы здесь? Why are you here?
Идите отсюда! Get out of here!

Under, from under, behind, from behind

Location and motion phrases regarding "under" and "behind" show a similar triple distinction.

If you go "to" a place using… then you'll be "at" that place using… and you'll return "from" that place using…
за + acc за + ins из-за + gen
под + acc под + ins из-под + gen

Examples:

Машина заехала за магазин. The car went behind the store.
Я припарковал машину за магазином. I parked the car behind the store.
Из-за магазина выехала грязная машина. A dirty car drove out from behind the store.

Кошка залезла под диван. The cat crawled under the couch.
Кошка прячется под диваном. The cat is hiding under the couch.
Я вытащил кошку из-под дивана. I pulled the cat out from under the couch.

Where English and Russian idioms don't match

Note that in Russian you are "behind" a corner, not "around" a corner.

Машина заехала за угол. The car went around the corner.
Я припарковал машину за углом. I parked the car around the corner.
Из-за угла выехала грязная машина. Around the corner came a dirty car.

Similarly in Russian one sits "behind" a table, not "at" a table.

Бабушка села за стол.¹ Grandma sat down at the table.
Бабушка сидела за столом.² Grandma was sitting at the table.
Бабушка встала из-за стола. Grandma got up from the table.

¹ The verb садиться/сесть 'to sit down' is conceived of as a motion in Russian and thus must be complemented by a motion phrase.

² The verb сидеть/посидеть 'to be in a seated position' is conceived of as a fixed position in Russian and thus must be complemented by a location phrase.