First, check the water line attached to the back of the refrigerator for good water flow. To do that, first turn off the water supply valve. Then remove the water line from the back of the refrigerator. Next, place the water line into a bucket and momentarily turn the water valve back on to test the flow. If the flow is poor, you need to repair, clean, or replace the tubing or the shut-off valve that supplies the water. If the flow is good, you may have to replace the water inlet valve.
The ice and water-dispensing system of your refrigerator is quite complex. Many components work together to provide the ice and water. Aside from a simple problem of a leaky water tube or a jammed ice chute, most other components are not user serviceable.