If you have a classical guitar with a bridge like the one pictured below - you have to tie them a knot at the bridge.
I found some tutorial explaining how to do it.
Remove the old string (if you haven't already).
Pass one end of the new string through the hole in the top of the bridge, in the direction away from the soundhole. Leave about 1-1/2 inches sticking out the rear of the hole.
Secure the string by bringing the short end over the bridge and passing it under the long part of the string.
Then pass the short end under, over, and then under itself, on the top of the bridge.
Pull on the long end of the string with one hand and move the knot with the other to remove excess slack and cause the knot to lie flat against the bridge.
If you have a pinless bridge on a steel string guitar such as those found on many Breedlove guitars and some Takamine guitars, you pull the strings through the hole being sure to protect your guitar's finish from the steel strings in the process. Here is a YouTube video showing how to do this on a pinless bridge for steel string guitar.