Covalent bonds happen between two non-metals.  One of the most common of
these is water (H
2O).  First lets look at the two atoms involved.
Remember, hydrogen fits well in either group 1 or group 17, in the case
of bonding it behaves like a halogen (group 17).  This means that can be
considered to have space for one more electron in it's outer shell in order
to have a full set or it can lose one electron to have an empty shell!

Notice that the nucleus is
not shown, that is because
the nucleus doesn't effect
the bonding.

With 6 electrons in its
outer shell, it has two
spaces to fill.  One on the
top and one on the
bottom in this picutre
Covalent Bonds - The Atoms