This isn't exactly a trick but more of a long term cost savings thing.
Ditch the inkjet and get a laser printer. This mainly applies if you are okay with black and white printing only. You can usually find a black and white laser printer for $50-75 if you're willing to jump through a small hoop (like print a coupon or submit a rebate). The toner lasts forever (well, many many times longer than an inkjet), and I don't think they "clog" or "dry out" in my experience. And I have been successful in replacing my toner with a generic toner for $35 or so, which is not a whole lot more than generic inkjet cartridges that seemed to dry out every 2 weeks. I think the toner works out to roughly a penny per page printed ($35 for 3000 or 5000 sheets IIRC). One potential downside is that the laser printer may be bulkier than your inkjet.
Retired in 2013 at age 33. Keeping busy reading, blogging, relaxing, gaming, and enjoying the outdoors with my wife and 3 kids (4, 10, and 11).