Rewrap the male pipe threads with thread tape going clockwise as you look at the end of the pipe, the way the fitting turns on. Tape wrapped the other way will loosen as the fitting is tightened.
Turn the water off at the shutoff valve before you take anything apart.
Check these in order
The tape went on the wrong way
How to tell: Unscrew it: the tape is bunched up, shredded, or pushed off the threads.
Fix: Clean the threads and rewrap clockwise, following the thread spiral, starting at the first thread. Tape should never hang over the end, where it can shred into the water.
Too little tape
How to tell: Only a single thin layer, or bare patches on the threads.
Fix: Add wraps. Swagelok calls for two to three, Oatey’s guide for two to four, and its FAQ for 3 to 5 on 1/2" to 1" pipe threads.
Tape on the wrong kind of thread
How to tell: The leaking joint is a hose connection, a supply line nut, or a compression fitting (a nut over a brass sleeve).
Fix: Take the tape off. Tape goes only on male tapered pipe threads, never on compression or flare fittings. Hose joints seal with a washer and supply lines with built-in washers.
Hose thread joined to pipe thread
How to tell: One side says NPT, MIP or FIP and the other is a hose fitting. If neither is marked, use the pipe thread size finder.
Fix: They don’t mesh, and tape won’t fix it. Use a hose-to-pipe adapter: see garden hose to 1/2" pipe.