for non-AE characters (everybody but the twins, E. Ryu and Oni), their costume and color files are in the resource/battle/chara directory.
The files are numbered corresponding to “costumes” (the actual 3D model) and “colors” (the painted textures that go onto those models). For example, any files named ZGF_01.* are parts of Zangief’s first (default) costume, while ZGF_01_01.col.emb and ZGF_01_01.obj.emm are the color files that correspond to Zangief’s first color slot for the first costume. ZGF_02.* files are the second costume (a.k.a. Alt 1), and ZGF_02_02.col.emb and ZGF_02_02.obj.emm are the files that represent the second costume’s second color slot, and so on.
Most of the skins currently on the wiki do not include costume files and are meant to be used with the standard Capcom costumes. In this case, you would only have–for example–the ZGF_01_04.col.emb and ZGF_01_04.obj.emm files, which are meant to be used with the first (default) costume and overwrite the fourth color slot. If you would rather it go into another slot, you can just rename them (e.g., ZGF_01_02.col.emb and ZGF_01_02.obj.emm if you want it to go into the second slot instead).
Likewise, if you download a mod that contains RYU_01.bsr, RYU_01.nml.emb, RYU_01.obj.emo, RYU_01.shd.emo (the costume files), as well as RYU_01_03.col.emb and RYU_01_03.obj.emm (the color files), they will all go into resource/battle/chara/RYU and replace both his first costume and third color. As before, you can rename them to overwrite whatever you want.