We have a loud hum on our phone line. ATT says the problem is in our wiring and is probably due to the line being grounded. Any suggestions for how I find the problem?

Take a corded phone to the gray box outside at your house. You will need a flathead screwdriver. On the phone box, you will normally see a side labeled customer access. Open that side of the box. Once open, you will see a jack that you will plug the phone into. If there is something plugged into it, just unplug it and plug in the phone. Check to see if the hum is still there. If it is there, the phone company (ATT) is responsible. If the hum is not there, you do indeed have a wiring issue that may be your responsibility. Check you phone bill to make sure you are not paying for wire maintenance. Make sure that if you unplugged anything from the jack outside that you plug it back in before closing the box. While the box is open, check to make sure there are no frail or corroded wires in there. You can unscrew the connectors (one at a time) and clean them up and tighten them back down. Now close the box and go back inside and try again to get the hum. Let us know from there...

If you only need 1 phone line, you may try using Yellow/black pair and rewire all jacks
Yellow wire to red on phone jack and black wire to green on phone jack.
To determine which wire is touching ground. Telephone Handset to monitor line, Disconnect
One wire, Hum gone? That is the wire. Usually if both were shorted to ground, Phone
Would ring busy.

My house, I would remove all jacks. If probem not found yet, disconnect from jacks, and disconnect at Telco Box "D Mark" all wiring and verify integrity and isolation between all conductors, and isolation between all conductors and ground (third prong from electrical recpticle). Extension cord may be used as ground reference if verified intact with meter(voltage between hot and ground at end of cord, then good reference point.)