Content in general:
Respect the ReadMe files that come with the content! Some folks are nice enough to share their stuff so it's only fair they can set the rules for its usages. The ReadMe breaks any rule that follows below if it contradicts it! If it just fails to mention something mentioned below, abide by these rules!
1. If you download something from here and you use it in your project, give it credit! Drop a line in your readme where you mention the piece of content you used and who made it.
2. No money is to be made from the content provided here. Do not sell it and do not sell your project if you used the content!
3. If you give the content to anyone else always include the ReadMe file that came with it. You don't have to do that if you distribute your project using the content. Only do it if you are passing on just the content.
Content for UT and UT2004
If textures come as a utx file, etc. then you should copy over the pieces you need into your own package or into the mylevel package of your map. You can do that by opening the downloaded package in the respective browser in UnrealEd, select the piece you want to have, click Edit, Dublicate and enter the destination package's specifications. Don't forget to save your own package when you are done!
Don't dump the downloaded packages into your UT folder and forget about them because everytime someone wants to have that map they have to aquire the packages as well. With lots of packages that's a bit of a hassle. Save yourself and the end-user the trouble and use as little packages as possible.
StaticMeshes can't be "duplicated" like this. To move them to another package place them into your level once, rightclick them and "convert" them to a StaticMesh. They are StaticMeshes already but by "converting" them you can enter new package and name details. Use that to move it where you want it to have. Delete that StaticMesh from your level afterwards or it will still require the downloaded package! Only place it from your own package then.
2. Inside a map-file
If your content comes inside a small example-map consisting of basically nothing but the content you want to have, you can simply copy and paste it from there to your own map in most cases. If you run into trouble don't hesitate to ask the poster of the content for guidance.
If it's a model that comes as a brush or as brushes, it might be a good idea to convert it to a StaticMesh before you use it to avoid potential BSP-errors and to benefit from the decreased performance hit.
Until now those are the only types of content provided. As soon as different types show up the list will be updated. If you find a topic in here and you don't know what to do with the files, ask in that topic. Someone is going to help you and the information provided there will be entered into this list here.