Turn the boiler off, if the water is hot in the loops, you might want to wait awhile for things to cool off as it can be messy removing an expansion tank, and you don't want to scald yourself. You should never get any water out of the air fill valve...if you did, the bladder is leaking - it may be slow, but that's all it takes. If the tank ever fills up with water it is bad. If the air leak is small, it may take awhile, and it may only leak when things cycle a bit, but you should never get water on the air side. Without the proper amount (pressure) of air in the tank, when the boiler comes on and the water expands, it will force the excess out of the relief valve to lower the pressure. When the boiler shuts off, things cool, and the water contracts, so without that flexible air cushion from the bladder in the expansion tank, it might then just try to add some water from the autofill valve.
Close any valves you can to help reduce/prevent water from draining from everywhere to include the autofill (if you have one). Unscrew the old tank, and on the new one, before you install it, pump it up to the normal BOILER water pressure, which is typically somewhere around 15psi, but you need to know that value (NOT the supply water pressure, which the heating loop should never see). Once you have the new one on (remember the pipe dope and/or tape), turn the water back on and open any valves, and purge air from your system, then turn the boiler back on.
If you're lucky, the relief valve will close and seal...if not, you should replace it.