What types of programs/model editors do I require to start modding the game?
You will need a different set of mod tools depending on which game you're modding.
Here's a list of tools you can download from the site.
http://www.swbfgamers.com/index.php?action=downloads;cat=3
For Battlefront 1 modding try this: http://www.swbfgamers.com/index.php?action=downloads;sa=view;down=1219
For Battlefront 2 modding try this: http://www.moddb.com/games/star-wars-battlefront-ii/downloads/star-wars-battlefront-ii-mod-tools-pc
Do I need any tools to change what the clones look like?
When I try to launch the tools, it says binkw32.dll was not found, is there a way I can find it?
What do you mean by changing what the clones look like? Do you mean changing the actual clone trooper model or just giving them a new colour/skin? If you're just retexturing the clones, all you will need is a photo editing program like GIMP or photoshop. If your making changes to the models you will need a 3d modelling program.
Here's a thread releasing to your binkw32.dll error: http://www.swbfgamers.com/index.php?topic=9220.0