Follow the install directions. They will tell you which files to upload and where to upload them to.
If there is an images folder, the files in there most likely need uploading to the images folder on your FTP. If there is a skins folder, the files in there get uploaded to the skins folder on your FTP, and so on. The files are usually in the folders they need to be uploaded to.
You can do both, they'll both work, however if you've got modified versions of the phpBB installation on your servers, such as exisiting mods and you update the fresh ones you downloaded from phpbb.com then they won't be there and can cause a few conflicts. If anything it's best to download them from your site, most of them are under 1mb anyway.
Remember to always back up your files. There are some sites which offer modification installation for their members. That would be something you might want to look into with the more advanced modifications.
My best advice to you is start practicing installing easy modifications and work your way to the more advanced - and always learn from your mistakes. Soon enough, you'll get the hang of it 😉 Good luck!