I just bought 5 boards from Allelectronics.com like this. I decided to make a circuit that involved ICs. When I attempted to solder the circuit onto the board I realized that once you solder the IC on, as far a I can see, you can't wire components to the pins because the solder sticks to the separate holes. So my question is how do you solder components to ICs? This should be easy I just don't get it because I am a newbie to prototyping.
In a perfboard you typically either bend unused leads or use wire to connect the different holes and then solder the wire and the pins together at a hole. You shouldn't use solder as some kind of interconnect trace like you're suggesting.
Here is a video showing proper perfboard construction.
There are perf boards available that have the holes connected together in the same pattern as the plastic breadboards, so you could easily transfer a breadboard project to a more permanent perf board design.
Vero Board has strips of copper connecting all holes in a row (or column, depending on how you hold the board). You cut away the copper at a hole where you don't want a connection - Vero makes a special tool for this, but a 3/16" drill bit (or even an Exacto knife) will work.