Some mods don't keep the necessary file structure and you need to put them there yourself. Here's how it works:
A mod is generally composed of two parts:
1) Ruleset, a single file which adds or changes new elements,
2) Resources, which are graphics and sounds. (Sometimes there's none, if the mod is purely data-based and doesn't introduce new graphics and such - for example something that gives more money to X-Com wouldn't need any resources, but something that introduces a new gun would.)
The ruleset is a file with a .rul extension which has to go to the openxcom/data/ruleset folder.
The resources are a folder, sometimes with subfolders, which has to go to the openxcom/data/resources folder.
After copying both to to the right location, remember to enable the mod in your game menu under "Mods".
Finally, always read the readme file, if the mod has it. Some mods don't have one (bad modder! bad!), but luckily they're rare.