Learn Hardcore Serbian: Pridruži nam se.

Pridruži = join, in the imperative (a command/invitation), addressed to one person informally
nam = to us
se = a reflexive particle that belongs with the verb pridružiti se

So word-for-word, it is something like Join yourself to us, but in natural English it is simply Join us.

What is the dictionary form of pridruži?

It comes from the verb pridružiti se.

That is the form you would look up in a dictionary. The sentence uses the 2nd person singular imperative of that verb:

Why is se there if English just says join us?

Because pridružiti se is a verb that normally includes se in Serbian.

This se often does not translate directly into English. It is just part of how the verb works. Many Serbian verbs behave like this.

So you should learn it as a whole unit:

In this sentence, se does not mean yourself in a strong literal sense; it is mainly a grammatical part of the verb.