A rag and mineral spirits is probably good enough for a start. If you are using tig you may need to do more. Since said rag is quite flammable you will want to protect it from welding sparks either by wiping everything first, and then removing all flammables before starting to weld, or by keeping the rag in a fireproof container such as a paint can with a lid while welding.

If this is a large operation disposal of used rags and solvent may have environmental implications.

Bill