Learn French: Je vais acheter un petit bateau. - I am going to buy a small boat.

This is how the near future tense (le futur proche) works! Just like in English ("I am going to buy"), you only conjugate the helping verb. Here, aller (to go) is conjugated as vais (I am going), and the main action verb acheter (to buy) stays in its infinitive (unconjugated) form.

Does Je vais mean I am physically traveling somewhere to buy the boat?

Not necessarily! Just like in English, "going to" is used here to talk about your future plans. You might be buying it online from your couch. It simply indicates that the action will happen in the near future.

Do I pronounce the "s" at the end of vais?

Yes, you do! Normally, the "s" at the end of vais is silent. But because the next word (acheter) starts with a vowel, you connect the two words. This is called a liaison. You pronounce the "s" like a smooth "z" sound connecting right into the next word.

I thought French adjectives usually come after the noun. Why is it un petit bateau instead of un bateau petit?

You are right that most adjectives come after the noun in French! However, there is a small group of common, short adjectives that always go before the noun. They usually describe Beauty, Age, Number, Goodness, or Size (often memorized with the acronym BANGS). Since petit describes Size, it steps in front of the noun.