I love screen printing. You can acheive vibrant results in a short amount of time. (Especially when you compare it to the lithography printing process!). This print is on my Etsy site as well. For the basic screen printing process, there isn't any acid to deal with or etching to master. The printing process is simultaneous with the creation process so it's instant gratification!
Our print teacher taught us the reduction process. You start by laying out your lightest color ink over your entire paper (except where you have already stopped out if you wanted to keep it white). As you transition to darker colors, you "stop out" what you don't want covered if that makes any sense.
So I did the light orange/yellow ink first. Then whatever I wanted to remain that color I applied a resist to my screen so those areas I wanted to remain that color wouldn't be hit with ink. Since you're printing an edition of at least 10, and a few extra for consistancy, you need to apply your ink to each piece of paper before stopping out your color. It's tricky to make sure your registration is consistant so all your layers of ink line up correctly. It makes much more sense in my head, it generally does.