Quick answer
Liking someone is нра́виться (dative), going out together is встреча́ться, and люби́ть is a much bigger word in Russian than “love” is in English.
The stages
The people
What you say
The stages in sentences
друг is not “boyfriend”
Мой друг means my friend, including a male friend of a woman. A boyfriend is мой па́рень and a girlfriend моя́ де́вушка. Saying мой друг about a partner will be understood as “a friend of mine”.
люби́ть is heavier than “love”
English says “I love this café”. Russian uses люби́ть for things too — я люблю́ ко́фе — but said to a person, я тебя́ люблю́ is a serious declaration, not a casual warmth. Early on, ты мне нра́вишься is the right size.
Typical mistakes
Я люблю́ тебя́ — on a second date
Ты мне нра́вишься.
люби́ть is a much bigger statement in Russian.
Я скуча́ю тебя́.
Я скуча́ю по тебе́.
скуча́ть takes по + dative.
Check yourself
What does мой друг mean?