The key to downloading an item correctly is to read the description and notes left by the creator. Particularly, look at required downloads as, without these, your content will either not work correctly or it won't show in the game at all.
Note: required downloads can be items at TSR or other sites. Some artists might charge for their work on other sites but are only permitted to do so by EA for the first 21 days after release, after which time it must become free. If you find the content at TSR with off-site required items trapped behind a permanent paywall, please report the creation, and we'll investigate.
These are the typical types of downloads you'll encounter for The Sims:
1. Retextures of official content
Some creators simply retexture an item where the 3D mesh already exists in the official game or its expansion packs. This means you won't need to download a mesh because it already exists in your game. Many makeup and clothing, wallpapers, floor tiles, and terrain paints are retextures of official game content. Occasionally, a retexture might require a mesh found only in a specific game pack. If so, the creator must mention this on the item's download page. If they haven't, please report the creation, and we'll investigate.
2. Brand new content not already in the game
Some people make brand new content not already in the game. These files contain both the mesh and its textures together. Unless the creator has stated that any other download is needed, these can go straight in your game and will work as they are.
3. Recolors of other people's meshes
Many custom content creators allow others to make additional retextures of their meshes. These are not stand-alone. In order for a texture to work, you must also download the original mesh. The creator must state where to obtain the original mesh. If they haven't, please report the creation, and we'll investigate. If you forget to download the mesh, the content will not show in your game.
4. Lots, rooms and Sims
These creation types are 'containers' that bring lots of other content together. Some state that they've used no custom content at all (in which case they can be downloaded and installed as they are), whereas others will provide lots of links to all the content needed to make your download look exactly like that shown in the pictures.