I was able to get a whole year of printing out of a old deskjet that was thrown out by cleaning it up.
Step 1: Get to Reservoir
You want to first get to reservoir to clean up the caked ink that accumulates there from the ink cartridges. This means that you have to carefully take the printer apart and save all the screws and parts so that you can put it back together again. You may want to document this just in case you get interrupted or you forget what you did last.