Well I think it's pretty straightforward. Take out your ink container and simply rinse it with water. If you can't remove the ink cartridges, then put the entire pen in cold water for 24 hours. That should do it.
I clean vintage pens by putting them in water for some hours, and then clean the pen with a ultrasound cleaner. Often the procedure is done 2-3 times.
The pen must be completely clean from old ink, and no color should remain when soaking up water and releasing it again.
Perhaps you been using wrong ink? All ink dry out, but there's a big difference in tush and ink. All ink should be made to fountain pens. If you are using iron gall ink, it will likely cloak your ink flow.