Learn Russian: Может быть, он дома.

Может is the 'he/she/it' form of the verb мочь (can / to be able to), and быть is the infinitive for 'to be'. Literally, it means 'it can be', but Russians use it as a fixed phrase to mean 'maybe' or 'perhaps'.

Why does the sentence use дома instead of just дом?

Дом is the noun for 'house', but дома is a special adverb form that means 'at home'. You do not need to add a preposition like 'in' or 'at' before it.

Why is there a comma after Может быть?

In Russian, introductory words and phrases like может быть (maybe) or конечно (of course) are almost always separated from the rest of the sentence by a comma.

Where is the verb for 'is' in 'he is at home'?

In Russian, the present tense of the verb 'to be' (am, is, are) is normally left out. So 'he is at home' is simply stated as он дома (he at home).