It will happen, a big question is whether the first crews go willingly since it will certainly take many decades if not centuries.

The most likely vehicle is a solar sail like project starshot is based on. It would have to be enormous in size, very efficient, and we'd have to create ginormous lasers to accelerate it. And it would have to spend most of the voyage slowing in order to actually make orbit. For Alpha Centauri, which is a three star system it may need to fly very close to Centauri C (the closest star) and blow past it to do the same to the other two to slow down make orbit around one of them.