Learn Polish: Dzisiaj jesteśmy razem.

In Polish, the verb ending usually tells you who is doing the action. The word jesteśmy already means "we are", so the pronoun my ("we") is usually dropped. You would only add my if you wanted to strongly emphasize "WE are together" (as opposed to someone else).

How can I remember that jesteśmy goes with "we"?

Look at the ending! The letters -śmy are the special Polish tag for "we". As you learn more Polish verbs, you will see that adding -śmy is the standard way to show that a group including yourself is doing the action.

Does the word razem change if we are talking about a group of women versus a group of men?

No, razem ("together") is an adverb. Unlike adjectives or nouns, adverbs in Polish are fixed words that never change their spelling. It stays exactly the same no matter who is together.

Can I change the word order and say Jesteśmy razem dzisiaj?

Yes, you can! Polish word order is very flexible. Putting dzisiaj ("today") at the very front of the sentence just puts a little more focus on when you are together, which sounds very natural.