They form water and a salt through a reaction called "Neutralization Reaction".
The classical good old example to this is the reaction of Hydrochloric Acid (
Will break up into
And reacting them together will result in this attraction
Which will bind together and form this
So basically the reaction will be like this:
However, this is true for strong acids and strong bases reacting together. For other cases involving weak acids or bases reactions, check the links below.
Source & further reading: