gauge just means: how big will it really be?
if you make a cute stuffed animal, well 2 inches tall is pretty much as good as 4 inches tall. Not so on a garment or functional piece.
you work with patterns, so the pattern needs to tell you how much to make for what size (starting with easy things as scarfs and ending in fitted garments).
gauge means nothing else then: “how big is your stitch?”
one stitch is hard to measure. so we count the amount of stitches in 10 by 10 cm or 4 by 4 inches (about the same). And we count the rows.
then you know: wow, I am using a yarn that has 160 meters to 50 g, if I make 20 stitches on needles size 4.5mm that is 10 cm wide. and I have to make 27 rows to get the same 10 cm.
this is, what I found out about my new yarn purchase on Saturday. And that made me very much smarter 
I make a pullover that is 42 cm wide. so I need 84 stitches (42 cm / 10 cm * 20 stitches).
I added one stitch for reasons of my pattern making. and there you go: 85 stitches wide = 42,5 cm (for a child).
now, smaller needles or thinner yarn (or both, of course) would make my sweater smaller. Bigger needles or thicker yarn would make it bigger.
If I used a pattern and it would have told me 22 x 29, for example, then I would have tried needles a bit smaller. Maybe 4mm or 3.5mm. until I get it right. or it might have told me 12 x 16 - then I would have given up on that yarn, because that would be too lose.
Every knitter is different in tension and stitch size. Every combination of needle and yarn and knitter therefore makes a relatively unique gauge.
If you want your pattern to come out right, you need to match yourself, your needles and your yarn to your project.
yarn mostly says on the roll, what gauge it gives with a certain needle size. But that is just generic and not the absolute point of it all. So do your swatch.
And listen to suzees mantra about that: if you want to find out how many stitches there are in 4 by 4 inches, then knit a swatch bigger than that, at LEAST 4.5 by 4.5 inches, better 5x5. then count in the center of your swatch. End stitches are not acurate!
To measure and count: put a measuring tape or ruler on your swatch. lay it parallel to the row that you want to count accross. (no egde row). Then line up the “0” on it with the beginning of 1 stitch ( the top left of the “V” to the very left of your counting, if you do stochinette) then count to the 4 inch mark.
so, what did you get? sometimes it will not be a whole stitch in the end… so what? 20.5 stitches is a fine result. Just as 11 3/4 would be.
are you close to what you should have? or should you knit on with bigger or smaller needles and make a longer swatch? just try it out until it is right enough.
once I get the amount of stitches, I count the rows, because mostly you only get one of them “dead on” and the other close. I want my stitches dead on, since they matter much more for the fit. Length mostly is given in inches anyways.
the counting goes just the same.
NOTE DOWN what came out. Easy enough to forget. yarn, needle size, pattern (garter, stochinette, pattern… if you did any). stitch and row count.
then (I never cut the yarn on my swatches) rip out the swatch again and start your project with the right number of stitches and the correct needle size.
There is a lot of information about what you do if you can not line up your gauge. But if you can line it up: start your work.
If the yarn fits the project, it mostly will be easy.
on, and: CIRCULAR needles rule the world! for round AND straight knitting. Get some, take the treat.
I never could see why anyone preferred to make a hat flat and then sew it up. Knitting in the round is easier and when it’s done it’s done. You’ll love it.