Slowly, in context, and by zigzagging.
The King comes first in an official capacity, to have his picture painted, and as someone who does not trust easily. However, he comes to trust Velazquez through their time spent together, and through the conversations they have, as Velazquez reveals himself.
Velazquez proves himself trustworthy, carrying out tasks with political meaning (meeting Rubens, for example, or going to Italy). Juan plays a part, by healing the king's beloved dog on the hunting trip.