Your official signature depends on your specific role. If your name were Robert C. Smith, and the decedent were your father John A. Smith, you would sign as follows:
For better or worse, people often shorten their signatures: "Bob Smith, PREP".
Frequently you will be asked to have your signature "notarized", which means getting a local notary public to stamp the document with his or her seal, indicating that you provided proof of identity (for example, with a driver's license) when you signed the document in the presence of the notary. Don't sign the document ahead of time!
Typically, you can find a notary public at a local postal shop, in the office where you work, or just by doing a quick search on the Internet. The process is fairly quick, and will cost somewhere between $10-$20.
You can learn more about notarization on the National Notary Association web site.
Occasionally, you will be required to get a "medallion signature guarantee", such as when dealing with individual stock certificates.
This requirement is much harder to satisfy than simple notarization, because whomever provides the guarantee is basically on the hook for covering all of the value of the asset if it turns out there's a problem with your claims. Consequently, few people want to offer these services.
Your best bet is to go to your local bank where you have an established, long-term account, and try to convince them to do this for you. It's a good idea to call in advance, because many branches do not offer this service, and it's not uncommon for only one person at the branch to be authorized to perform the service: when that person goes on vacation, for example, no medallion signature guarantees are performed until he or she returns.
Oddly, while the medallion signature guarantee is much more meaningful, and much harder to get, it is not uncommon for it to be provided free of charge.
You can learn more about the medallion signature guarantee on the U.S. Securities & Exchange Commission web site.