Learn Hardcore Ukrainian: Петро любить жартувати.

Ukrainian doesn’t use a separate word for to with infinitive verbs.
The infinitive itself (жартувати) already means to joke.
So любить жартувати literally is likes joke-to, which in English becomes likes to joke.

What form of the verb is жартувати, and why is it used here?

Жартувати is the infinitive form (the “dictionary form”) of the verb to joke.
After verbs of liking, wanting, starting etc., Ukrainian typically uses an infinitive:

любити + infinitive – to like doing something
So любить жартувати is the regular pattern [likes] + [to joke].

What person and tense is любить, and how would the whole verb любити conjugate?