Telephone jacks have no working parts, so if one is not working, rather than fixing the jack, you must replace the jack (or the wiring connected to it). Most residential jacks are designated RJ11 and have four conductors, and when it comes to replacement, all jacks are handled the same way.
If a phone jack is broken, the culprit might be bent, broken, or dirty conductors, or a cracked or kicked jack. Or it might not be the jack at all; rather, it could be the wire or a problem at the demarc (the abbreviation for the "demarcation" device or point, which is where your telephone service provider's wiring responsibility ends and yours, as homeowner, begins).
Bent, Broken or Dirty Conductors
If somebody moved furniture or was very enthusiastic with the vacuum cleaner, the jack may have been hit or kicked but sometimes it's not obvious. Unscrew the jack cover and examine the wires that come out of the actual jack (the part where you plug in the connector cable). They should be clean, dry, and securely fastened without breaks. If this is not the case, replace the jack.
Video of the Day
Cracked or Kicked Jack
If somebody moved furniture, or was very enthusiastic with the vacuum cleaner, the jack may have been hit or kicked, but sometimes it's not obvious. Unscrew the jack cover and examine the wires that come out of the actual jack (the part where you plug in the connector cable). They should be clean, dry, and securely fastened, without breaks. If they are not, replace the jack.
If the wire is surface-mounted, follow the wire from the jack as far as you can. If the wire has been cut, squashed, or even bent severely at any point, the wires may be broken inside the outer jacket where you cannot see them, so replace that wiring.
If the wiring goes into the wall, something may have happened to that wire. Possibilities include rodent damage, lighting or other electrical discharge on that wire, burning or melting from some cause, or something else. It would be nice to know what the problem is, to keep your family safe; but in any case, the most important thing is to remove the wiring if you can and replace it. (If you pay your telephone provider a monthly premium for inside wiring maintenance or if you're willing to pay $100 or more, they can come in and fix it.)
At the Demarc
Most demarcs have only one place for your wiring to connect, so you should find a wiring breakout box where the wiring for all your extensions has its starting point. Examine the wiring for this jack's wire and confirm that it is not loose. If it is loose, screw it back on until it is secure. If it has broken, restrip and resecure the wire if you can. Otherwise, replace the wire.