Answer:
The short answer is, you don't.
When dealing with collectible items, any cleaning methods you may have available at home will almost certainly do more harm than good by damaging the item's underlying material. That's especially true with paper, wood, etc. Watch Antiques Roadshow some time and see the expressions of horror on the appraisers' faces when someone tells them they tried to "fix" an old painting or piece of furniture!
If you have bills that were printed before the 1960s they may be worth more than face value, but you'd need a professional appraisal or two before selling. You can always post questions here and get free estimates of course! If you decide to do that, be sure to include the following for each bill:
> Its denomination
> Its date
> Whether it has a small letter next to / under the date (not all bills do)
> Its seal color
> If it doesn't have a picture similar to modern bills, a description of the image(s)
Remember you DON'T have to include the serial numbers because that really doesn't provide any useful information about a bill in most cases.