I am 83 years old and it has been over forty years since I piloted an aircraft and would like to go back to flying again. I hold a single engine rating and had flown several hundred hours, but my log book is long gone. Much of my time was ferrying new Cessnas from Kansas to Houston for a dealer. Other than a physical and a checkride what would I realistically need to resume flying again without endangering myself or others?
Much has changed in 40 years, including airspace designations, ATC communications, and new regs. If I were you I would take an online Private Pilot Ground School to learn about all the new changes. These courses are not too expensive and it well worth the money.
The AOPA does have a Rusty Pilot Seminar as well (link).
Also it might be worthwhile just to sit in the passenger seat of a plane for a while to re-familiarize yourself with how it all works.
Certificate, Medical and Flight Review
FAR Part 61 explains what is needed to exercise the privileges of your pilot certificate. For this answer, I will assume that you are certificated as a private pilot.
Certificate: Your certificate does not expire, so, presuming you are still in the FAA database, you should be able to pay a small fee to have a duplicate sent to you, if necessary.
Medical: Here you have some options. As a private pilot you may now operate under sport-pilot regulations (day-VFR, restrictions on aircraft seats, weight and stall speed). The basic med rules are still less restrictive, and of course you may still obtain a third class medical for full privileges. If you think you may have trouble with a third-class medical, it would be good to research your options before scheduling an examination.
Flight Review: Finally, you must have a CFI endorse your competence with a flight review. This is normally a two-hour affair, one in the air and one on the ground, but in your case, as others have said, you may want to study and perhaps take several refresher flight lessons.