In general, patching is like connecting a plumbing (or electrical)
system - sound goes in, gets routed around (and modified), then comes back out. Mic ->
mixer/processing -> amp ->
speaker.
As far as patching into your
console, you may need to try a few different ways to get the handles that you'll mix the show with laid out in the most efficient arrangement. Take a lot of notes, or create a spreadsheet where you can
track where everything is plugged in. Don't be afraid to move it around if you think there might be a better set-up. Work toward making it as intuitive as possible FOR YOU. That could look very different from how I would set up my
console. Think about where your hands will be when you are mixing, and which mics you'll need to touch most often. Think about who is on
stage with whom - having those faders physically near each other on the
console will make it easier to mix.
In the (input) EQ department, a quick search yielded this result, which, although geared toward a worship situation, seems to be pretty great at explaining a lot of big concepts:
http://www.behindthemixer.com/mixing-vocals-the-ultimate-guide-to-eqing-vocals/
Overall, as the article states, less is more, and removing is better than adding. If that article doesn't make sense to you, search something like "live sound mix EQ" for dozens more good options!)
For output or
system EQ, if that is available in your space, put on a piece of music that you know well, that you think has great "sound". Take a picture of the
current settings, then start moving the faders around. Did what you did make it better? Worse? Find a spectrum analysis app for your phone and look at what's coming out. Huge peaks? Huge dips? Does it sound better or worse when you smooth those out? Use some science and some art to figure out what works in your room!
HTH,
Jen