Learn Croatian: Uvijek šetamo zajedno. - We always walk together.

In Croatian, you usually drop the subject pronoun (like mi for "we") because the verb ending already tells you who is doing the action. The ending -mo in šetamo clearly means "we walk".

What is the dictionary form of šetamo and how is the "we" form made?

The dictionary form (infinitive) of this verb is šetati. Since it is a regular -ati verb, you find the "we" form by dropping the -ti from the infinitive and adding -mo, which gives us šetamo.

Does uvijek (always) have to go at the very beginning of the sentence?

Not necessarily! Croatian word order is quite flexible. You could also say Šetamo uvijek zajedno, though Uvijek šetamo zajedno is the most natural and common way to build this sentence.

Does the ending of zajedno (together) change if the people walking are male or female?

No. Zajedno is an adverb, which means it describes how the action is done. Adverbs are fixed words in Croatian, so zajedno never changes its ending no matter who is doing the walking.