According to the scriptures, Sakyamuni Buddha would travel in the normal way by walking. Progressing slowly from one city to another, helping people along the way.

When he is aware of someone who is ready to receive his teachings, he would travel alone to meet that person. Appearing at their doorstep or waiting for them along the road. Buddha would survey the world using his clairvoyant mind every night to determine any potential student to be taught. Then he would go meet that person.

On special occasion, when there are special needs, Buddha may use his supernatural power to bend distance. So that he can cover extra distance even though he is walking in his usual pace. This ability is fully demonstrated when he converted the serial killer Angulimala into a monk. No mater how hard Angulimala chased and ran after the Buddha, he cannot catch up with the walking Buddha.

Buddha can also teleport. Disappear from one place to re-appear in another. This feat is utilised when there is a need to do so.

Buddha have the ability to levitate and fly in the air. Likewise for some of his enlightened disciples. Imagine the Buddha flying in front , followed by flying monks and nuns behind him, in an orderly manner.

He can also send a copy version of himself and projecting it into another location. The projected version was an exact duplicate and no different from the original with full capabilities of a Buddha. (Not  appearing like a puppet but its own master with full Buddha abilities)

His abilities are too numerous to recount and I am sharing what I can remember from my readings. Buddha is my favourite super hero. Far greater than any marvel character.