Quick answer
Я учу́ ру́сский язы́к
ya uchú rússky — and the sentence that gets Russians on your side
The options
Я учу́ ру́сский язы́к.I am learning Russian.
Я изуча́ю ру́сский.I study Russian. — a bit more formal
Я учу́сь говори́ть по-ру́сски.I am learning to speak Russian.
Я то́лько начина́ю.I am only just starting.
Я учу́ ру́сский три ме́сяца.I have been learning Russian for three months. — present tense in Russian
Three verbs, one English word
Учи́ть = to learn something specific. Изуча́ть = to study a subject. Учи́ться = to be a student somewhere. Only the first two take “Russian” as an object.
The tense that surprises English speakers
For something that started in the past and still goes on, Russian uses the present: Я учу́ ру́сский год — “I have been learning Russian for a year”. No perfect tense involved.
What you hear back
Вы хорошо́ говори́те!You speak well!
Молоде́ц!Well done!
Ско́лько вре́мени вы у́чите?How long have you been learning?
Typical mistakes
Я учу́сь ру́сский.
Я учу́ ру́сский.
учи́ться takes no object.
Я учи́л ру́сский год — still learning
Я учу́ ру́сский год.
Still going on means present tense in Russian.
Check yourself
Which sentence means “I am learning Russian”?
учи́ть takes a direct object; учи́ться does not.