Learn Spanish (Spain): Empiezo a dar un masaje.

In Spanish, the verb empezar (to start) requires the preposition a when it is followed by an infinitive (a verb in its basic, unchanged form). So, "to start to give" becomes empezar a dar.

Why is it empiezo and not "empezo"?

Empezar is a stem-changing verb. In the present tense, the second e changes to ie for most forms, including the "I" (yo) form. That is why it becomes empiezo. It only stays as an e in the "we" (nosotros) and "you all" (vosotros) forms.

How would I add an adverb like suavemente (gently) to this sentence?

Since you are learning about -mente adverbs, it is helpful to know where they go! You can place suavemente right after the verb it modifies. If the starting action is gentle, you could say Empiezo suavemente a dar un masaje. If the giving of the massage is gentle, place it at the end: Empiezo a dar un masaje suavemente.

Why is it un masaje and not "una masaje"?

The word masaje is masculine, which is why it uses un. A great trick to remember is that almost all Spanish nouns ending in -aje (like viaje or garaje) are masculine.