First, download piecemontee's SF4 Assets Explorer. This is the cornerstone of model editing: http://sf4mods.pbworks.com/Utilities#piecemonteesSF4AssetsExplorer
Next, you'll need a 3D modeling program. I use the open source Misfit Model 3D because it preserves some coordinates and whatnot that seem to get dropped from other, more capable programs, such as 3D Studio Max (from what I hear from other modders; I have no experience with 3DS): http://www.misfitcode.com/misfitmodel3d/download.html
Once you have your tools, open the SF4 Asset Explorer and click 'Load file...'
Now, navigate to the costume file you wish to edit:
Click on the plus signs next to the path and the first entry marked "#EMB ([***]_01.obj.emo):
If you click on a model element, it will isolate it from the overall character model, like so:
Now, right-click on the element's name and select "Extract file...":
Name it something informative and give it the extension ".obj":
Next, open the file using Misfit Model 3D:
From here, you can move around vertices as much as you want, but you CANNOT add new ones or remove any. The number must stay EXACTLY THE SAME or you cannot re-inject it back into the model:
After you're finished editing, save the file and uncheck the option to "Save normals" (actually, I don't think this matters):
Now, back in the SF4 Assets Explorer, select and right click on the element you edited and choose "Inject file...":
Select your edited model and click "Open":
The program will automatically create backups whenever you inject models, which is nice, but you should still be careful about overwriting because there is no "Undo." This edited model should now be ready to drop into your C:\Program Files\CAPCOM\STREETFIGHTERIV\Battle\Chara\*** folder to replace your old costume file.