I loaded Morrowind on my Dell XPS laptop, which is about 3 years old and runs Windows Vista. I've successfully loaded the Morrowind GTY edition and the Morrowind Code Patch by Hrnchamd. The guides I've read suggest also installing the Morrowind Patch Project files, but when I try to run the .esm file it asks me what program to open it with and I'm not sure what to do with that. Any suggestions?

You can't just open the esm. When you run Morrowind, in the launcher under data files just put a check beside the esm. You do that with nearly all mods. The construction set can open the esm, but there's no reason for you to do so.