What Size should my DDS Textures Be?
For meshes, DDS images (see also: Sims 3 Wiki DDS page) must be fixed sizes of one of 2, 4, 8, 16, 32, 64, 128, 256, 512 or 1024 pixels. These sizes correlate with a Sims game tile (e.g. floor tile) which is 256 pixels by 256 pixels (walls are 3 x 256 pixels high). If you make an object that fills a floor tile horizontally (like a counter top), then that counter top must fill a 256 pixels wide area on your multiplier (see: What is a multiplier?).
How image sizes translate into mesh sizes in the game:
128 pixels (quarter tile) 256 pixels (1 tile) 512 pixels (2 tiles) 768 pixels (3 tiles) 1024 pixels (4 tiles - maximum)
What about 3 tile objects? Some objects are 3 tiles (columns are 3 tiles high, and some sofas are 3 tiles wide). However, there is no such DDS size as 768 pixels (3 tiles x 256 pixels). For 3-tile object sizes, use a 1024 pixel size but ensure 3-tile-wide parts of your mesh only occupy between 750 - to 800 pixels.
1024 pixels is the maximum size. If your mesh is larger than 4 game tiles in any direction (a vehicle for example), you will need to divide your UV map (and possibly your mesh) to fit within a 1024 x 1024 area maximum. For a good example of this, clone an EA vehicle and study how it is mapped.
Do my images need to be square? For patterns, yes (they should be 256 x 256 pixels). For all other creations, any combination of the above numbers is acceptable. As an example, the multiplier for the pictured ladder is 64 x 512 pixels (the ladder mesh is in two halves, both mapped to this same multiplier).
How to fit your UV map at the correct texture scale for the game Size is directly related to how much space in the game each part of your object will occupy. A floor tile is 256 x 256 pixels so you can use this as your guide. For example: the seat cushion part of this dining chair, from top down view, appears to occupy quarter of a tile in the game, or 128 x 128 pixels. Therefore, this part of the mesh also occupies approximately 128 x 128 pixels on the multiplier too.
For patterns, DDS (and PNG) images are always 256 x 256 pixels in size. No other size can be used.