Learn Russian: Завтра я зайду в супермаркет и встречу там друга. - Tomorrow I will drop in to the supermarket and meet a friend there.

The prefix за- on a verb of motion adds the meaning of dropping by, making a short visit, or making a detour. By using я зайду instead of я пойду (I will go), you are saying that the supermarket isn't your only destination for the day; you are just popping in for a little bit, likely on your way somewhere else.

Why do we use в + Accusative (в супермаркет) here instead of к + Dative?

When dropping in at a place or a building, you use в or на followed by the Accusative case to show your destination, just like you would with regular verbs of motion. You only use к + the Dative case when you are dropping in to see a specific person (for example, я зайду к другу).

зайду and встречу look like present tense forms. Why do they translate as future (will drop in, will meet)?

Both зайти and встретить are perfective verbs. Because perfective verbs focus on the completion or result of an action, they cannot describe an ongoing action in the present. When you apply standard present-tense conjugation endings to a perfective verb, it automatically forms the future tense.

Why is the word for friend друга and not just друг?