While it is true that "left" and "right" is one of the things that can't be transmitted to aliens in a distant galaxy by any digital information method anyone has found, it is NOT true that putting the propeller on an airplane backwards will make the plane fly in reverse. A right-handed screw is right handed from either end.

But are we going to wait until the faucet handle is off to ask if the faucet has washers in it that need to be replaced, or if it's one of the more common "plug valves" that requires O-rings to correct a leak?

How to Repair a Faucet (page 2 if the link doesn't take you there) shows a typical compression seal faucet, as it seems we've all assumed is the kind in question.

Depending on the type of handle, note the "packing nut" in the picture. Some faucet handles "shroud" the packing nut so you can't get to it without removing the handle, but for many, you can loosen the packing nut without removing the handle and screw the piston out, allowing you to replace the washer without the need to break the handle (which is always corroded on) loose.

The next page shows a "seat dresser" for cleaning the place where the washer makes its seal. Using one of these is a recommended step, but may not be necessary if the seat appears to be in reasonably good shape.

The following page has a discussion of replacement of the stem seal. If you use a gasket/O-ring type seal, it will be necessary to get that handle off the stem, but a "cord" type packing can sometimes be used without removing the handle, if the stem is long enough.

Note that handles are usually fairly easy to replace, so "break and replace" may be an ultimate necessity if the existing handles are too badly stuck and it really is necessary to get one off. If it does go that far, replacing the entire stem along with the new handle might be worth consideration. For most common faucets individual part replacements can be found fairly easily.

Although there is some discussion of "other types of faucets" on following pages, this article doesn't appear to show any illustrations. If you run into something different than what's shown, your best recourse probably is a visit to a good hardware shop where they can show you things until you find something that looks like what you've got. Places like Lowes and Home Depot generally have displays of common plumbing riggings hanging on the walls that may be helpful, but smaller shops likely can give you fairly specific help.

John