A wormhole begins life as a small quantum rift, a
hole in space-time which connects together two points.
Initially, these two points are very close together
(maybe an atom's width apart). These holes appear
randomly throughout the universe, last for a few
micro seconds, then vanish.
Advanced technology can be used to capture and
stabilise such a hole though. Once stabilised, the
mouth at each end can be grown by building a
framework of exotic matter around it. The two ends
can be pulled apart, but they are still connected
together similar to a pair of Quantum entangled
particles. Both ends of the wormhole are the same
point in space-time. It is not a tube or a gate
which teleports you from one end to the other. They
are the same point - just in difference places.
You can see through a wormhole, stick your head
through it, through a ball through it, fly a spacecraft
through it. You could stick it on the surface of a
planet and build a railway through it (this has been
done on several worlds).
What does it look like?
A wormhole is two dimensional, often circular
(though this is a feature of the framework that
keeps it open). Only a single face of the hole
can be passed through - the back side is a
space-time flaw that is impervious to most
physical effects.
The surface of the hole does not ripple or glow
or look anything other than an empty bit of
space. It is impossible to tell that you've
just passed through a wormhole except by looking
at outside phenomena (i.e. you are now in a
different galaxy).