After you find the will, then what? Well, of course you want to keep the original in a safe place, and make a couple of copies as well. But you actually shouldn't hang on to the will very long; instead, you should promptly file it with the local court.
(If there is no will, see What Does The Executor Do When There's No Will?)
In most states, anyone who comes into possession of an original signed will of a deceased person is required by law to file (record) it in the courthouse of the county where the person resided. Most states impose a deadline of ten to 90 days after the death, or after you receive notice of the death. The filing of the will starts the probate process.
If you don't file the will, it's possible that you could face a lawsuit from anyone who suffers losses as a result of your failure to promptly turn the will over to the court. For example, a creditor or someone who is supposed to inherit under the will could be harmed if it's not filed until the deceased person's property has already been distributed.
Depending on custom in the county, you'll deposit the document with the probate court, county clerk, or "register of wills." If you're not sure where to go, you can find out the right place by inquiring at the court. There may be a fee for filing the will, but it shouldn't be very high—about $20 to $50 is common. Some states or counties, however, don't charge anything.
Probate isn't always necessary—for example, it won't be needed if all or most of the deceased person's assets will pass through a probate-avoidance trust, go to a surviving co-owner by the right of survivorship (some retirement assets, for example), or be transferred by a beneficiary designation (like a payable-on-death bank account). But you should file the will even if you don't think there will be a probate proceeding. First of all, it's required by law.
Moreover, even if right now you don't think probate will be required, you might be wrong. For example, it's not uncommon to discover assets a few months down the road; their value may mean that the estate no longer qualifies for out-of-court transfer procedures or that you must probate the assets before you can transfer them to the deceased person's living trust. If you do need to begin a probate court proceeding later, you'll be glad you filed the will. If you had violated the law by not filing it, the probate court might refuse to appoint you to serve as executor.
If you're not going to be the one wrapping up the deceased person's estate, but find yourself in possession of the will, you should still file the original, as discussed above. Also send a copy to the person named in the will to serve as executor, if you know how to reach that person.