Learn Hardcore Russian: Я наслаждаюсь моментом.

The verb наслаждаться governs the instrumental case for its object. In Russian you “enjoy” something by using the pattern наслаждаться + instrumental (наслаждаться чем?), so моментом is correct, not the accusative момент.

What person, number, tense, and aspect is the form наслаждаюсь?

It’s first person singular, present tense, imperfective aspect.

Imperfective verbs describe ongoing or habitual actions.
The perfective counterpart is насладиться, which would focus on completing the action (e.g. “I will have enjoyed the moment”).

Is наслаждаться a reflexive verb? What does the -ся suffix do here?

Yes. The -ся makes it “reflexive,” turning “to enjoy” into literally “to enjoy oneself.” It shows the subject (Я) is both performing and receiving the action of enjoying.

Can I drop я from Я наслаждаюсь моментом?

Absolutely. Russian often omits subject pronouns because the verb ending -юсь already signals first person singular. You can simply say Наслаждаюсь моментом.

How would you say “I will enjoy the moment” in Russian?