The tank is located in the basement. I am guessing it was installed in 1989, when the house was built.
Can the tank be repaired? Or do I need a new one?
In either case, is this a job I can do myself? (I am pretty handy. I have quite a few tools, and have installed copper pipe and plastic drain pipe a number of times over the years.)
Do you have a manual for the tank, or can you find one online? Or just look to see if there’s a pressure relief valve somewhere, a likely and repairable cause of the leak.
There won’t be much of a manual, because all it is is a balloon in a tank. Aside from physical damage, the only likely source of a leak is one of the joints.
Not a pressure tank maven but they seem to range from around 150 - 250 dollars. At that price it might be wise to simply replace one that has given 24 years of service.
I don’t believe most residential-grade pressure tanks are repairable. 20 years seems to be an average lifespan. Replace it - put in a bigger one while you’re at it. That will increase initial and short-run water pressure and take some load off the well pump.
Quick test. There should be an air connector like the stem on a tire on the top of the tank. Use a screwdriver and quickly press in the valve core. If water comes out the bladder is ruptured.
The rubber diaphragm wears out eventually on these things. I replaced mine a couple of years ago; it would have been about 20 years old at the time. I think I only paid about $200 for it at the time, but I did have to also buy a pipe wrench for less than $20 I believe.