How you apply a patch depends on which platform the game is for.
The usual way of applying a patch to a PSX game is to copy an image of the disk [ISO/BIN] to your hdd using nero / cdrwin and then patching the image file. These types of patches usually come in PPF format [i.e. have a .PPF extension] and cannot be used without a PPF patcher program.
As you've got an .exe file - I'm going to assume it's not a psx game you're trying to patch.
The usual way of patching for these games is to first install the game onto your hdd using the install option. YOu then get your patch executable and put it in the main game directory (where the game was installed). Then, when you run this patch (double click on it) it modifies the game executable and the game is patched (usually to require no cd to be present or defeat copy protection).
So in short, all you have to do is double click on the patch executable once you've put it in the game's directory.
Hope this helps!