Start by checking the water supply going to the fridge using the technique of the Master:

• Turn off the water at the saddle tap valve.
• Disconnect the water line in the back of the fridge. Place the disconnected end in a bucket and open the saddle tap valve.
• Observe the flow rate–water should shoot out vigorously. If not, then the saddle tap valve is probably gunked up with sediment and you’ll need to replace it.

That should restore normal water pressure. You can buy a new water supply kit, which includes the saddle tap valve, here. More tips on the proper installation of a water supply line and saddle tap valve here.

If the water supply flow rate test, described above, appears normal, then the water inlet valve on the fridge may be gunked up with sediment. Here’s how we check for that:

• Reconnect the water supply line to the valve and turn the water back on.
• Disconnect the nylon tube from the dispenser side of the valve and replace it with section of tubing so you can out the other end in a bucket.
• Now actuate the water dispenser and observe the flow out of the tube. It should be the same as the flow you observed in the first flow test described above. If not, then you know the valve is restricting the flow–replace the valve.

The foregoing discussion is neatly contained in this haiku (inspired by Fixum in the Appliantology group forum):

Fridge water flows slow.
Saddle tap or solenoid:
it’s one of those two.