Learn French: Voici le modèle, est-ce que tu vas le dessiner ? - Here is the model, are you going to draw it?

When you have a conjugated verb (vas) followed by an infinitive verb (dessiner), the object pronoun goes immediately before the infinitive. So, to say "going to draw it", you put the le right before the action it belongs to: tu vas le dessiner.

Does the le in le dessiner mean "him"?

Here, it means "it". Le is the direct object pronoun for masculine singular nouns. Because it refers back to le modèle (a masculine noun), we use le to say "draw it".

Could I use Voilà instead of Voici here?

You could, but there is a slight difference. Voici means "here is" and draws attention to something right next to the speaker. Voilà means "there is" and points to something a bit further away. Since you are presenting a model right in front of you, Voici is the most natural choice.

How does tu vas dessiner translate to "are you going to draw"?

This sentence uses the near future tense. It is built by taking the conjugated verb aller (here, tu vas meaning "you are going") and adding an infinitive verb (dessiner meaning "to draw"). Together, they mean "you are going to draw".