special relativity - How time dilation happens by velocity?

i got many explanation and proving that relative velocity causes time dilation. Einstein's moving light experiment proves it. but that is a clock works with light detector. as detecting the light gets latter the clock works slowly. but in reality how a real watch can be slowed down? And won't the man feel that the time is moving slowly as he knows the general speed of the clock? Sources says that if a man goes to space with very high speed if he returns after few years as his clock moved slowly earth would be moved for many years forward. But my doubt is won't he feels the fact that his clock was slow and he spend many years in space? If he won't feel it how does it happens? and how is he not getting older?