It's really easy! All you have to do is download BOINC here and Gridcoin here.
Then you go through the installer. Let's use BOINC first. Just open up the installer, and it'll tell you to start a project. Sign up for SETI@home, it's a widely-supported and big project. Sign up at the website, log in with BOINC, and you're all set! I personally use the Advanced View (Ctrl+Shift+A), but you can do whatever you want.
next, we work on Gridcoin. Go through the installer, and you HAVE to run Gridcoin as Administrator. If the New User Wizard doesn't open up automatically, go to the "Advanced" tab, and click New User Wizard. Enter your BOINC information, and make sure you join Team gridcoin on your current project page (for instance, setiathome.ssl.berkeley.edu) and then you'll get rewarded to help research!
The Gridcoin website has all this information too, so go check that out!
Now all you have to do is wait for the Gridcoin wallet client to sync the blockchain (this usually takes a while, so be patient) and voila! You now have Gridcoin and BOINC installed! Oh, and don't forget the Android app!
That's basically all it takes to get Gridcoin and BOINC up and running!
How do you know to choose which BOINC projects gives out the most coins?
Good question! The entire BOINC system is based around a work unit. The harder the task, the more points you get. However, I would recommend that you do some easy work for SETI@home. In the project preferences, you can deselect the "Long runs" option and instead choose the "Short runs" option. It doesn't matter which projects you do, but on how much work you've done on it. Choose any project you want, but make sure your device can handle it.