14 Then Jesus, having found a young donkey, sat on it, even as it has been written:
15 Don not be afraid, daughter of Zion; look your kings comes, sitting on a young (a colt) donkey.
16 At first the disciples did not understand these things, but when Jesus was glorified they remembered that these things had been written about Him, and the things that they did to Him.
The other gospels give us more information about how Jesus acquired the donkey. He told two of His disciples to go into the village ahead of them. Mark and Luke mention Bethphage and Bethany, but do not say which of the two they should go to. However, Mathew tells us that it was Bethphage.
It was in the village that they would find the donkey and they were to tell the owner that the Lord needs it.
We do not know whether or not Jesus had made a prior arrangement with the owner, or if He was acting within the gift of knowledge.
Sitting on a donkey was not an unusual thing for a king to do. We are not familiar with our queen riding on a donkey. When she was able she would ride on a horse, an animal of noble character.