First thing you should do is calibrate your monitor (if you haven't) which is adjusting color/brightness and cast to attempt to get as true as you can to approximate real life. This will definitely improve your accuracy in the photo, or the art you hope to print. The best way to do that is to use a calibration tool. These vary in range of price, but it's the most accurate method. Datacolor Spyder is a popular brand.
But there are also some online tools for calibrating which could be a good starting place. Do a google search on computer monitor calibration tools. Next thing you need to do is to make sure your printer color profile is properly set for the ink and the substrate or PAPER you're printing on. It's called an ICC profile. Haven't read this link, but it's maybe a place you can start: https://www.dpreview.com/forums/thread/3805648
I guess this is the time say it will be different for PC or Mac. And it may vary depending on editing program you're using, Photoshop, Gimp, etc. What you're dealing with here is output settings, matching the right ICC profile to the right printer and paper/substrate. Realize that your paper will "suck up" ink at varying rates depending on it's composition, coated, heat/cold press, etc, ad nauseum. BUT in their infinite wisdom most printer companies, especially Epson (I have two, a quick and dirty and my trusty Photo R1800) provide various profiles for different papers using their inks because so many commercial printers use them. You should be able to get the latest update on the Epson site.
When you've downloaded the necessary ICC profile for your paper, you will then go into your editing program and do what is called a "soft proof". This is a neat trick where you clone a separate copy of your original work (photo) and then apply the profile to it wherein the software shows you what it projects what it will look like printed on your paper. You will then see if it's too dark, or that red isn't right, or it's too light (rarely) and can adjust your original to approximate the clone. THEN you get to print. Youtube is your friend, there are tutorials on most of this stuff :-)
If this sounds like too much information...well, it probably is. And my apologies if Mark has addressed this elsewhere. But I thought I would reply anyway. I've had quite a few years doing pre-press computer graphic art for remote output, everything from newsprint to coated to giclee on fine art paper.