When you first start to make a project like mittens or a hat, your pattern will likely instruct you to cast on and then join to knit in the round. What it often leaves out are the instructions on how to join your knitting to knit in the round.
There are a couple of ways for joining knitting in the round and like a lot of knitting choices it comes down to your personal preference and comfort level. No matter how you join your stitches to begin knitting in the round, you need to make sure of one thing first: make sure your stitches are not twisted. Lay out your stitches, whether they're on circular needles or double points, to make sure they're all in a neat row with the bottom edge at the bottom.
If you are working on circular needles, you'll need to space out your stitches across the entire needle so that the two end stitches can meet. Sometimes that first row can feel tight, but if you're using the length of needle your pattern called for, it will be ok. The stitches will stretch out as you work.
One way of joining your knitting is to just start knitting. The needle that has the stitch with your working yarn goes in your right hand, the other needle in the left. Then just knit (or purl) into that first stitch on your left hand needle and go from there. With this method, tension will be important. You want to make sure that there isn't a big, loose yarn gap between the last stitch of the cast-on row and the first joined stitch. To avoid that, pull your yarn tight after knitting that first stitch. Also, don't forget to place a marker right before that first joined stitch.
My personal choice for joining in the round is to slip the last stitch on my right hand needle onto the left hand needle and then slip the first stitch from the left needle onto the right, passing the first slipped stitch. With this method, you're just switching the two end stitches. I have never noticed a difference with which stitch I slip first. After switching the two stitches, place your stitch marker and begin knitting. Depending on how you cast on, your working yarn could wind up with the stitch on either needle and frankly it doesn't much matter. You can switch your needles at this point so the working yarn is on your right needle. Or if the yarn wound up on the left needle, you can still just work your first stitch on the left needle. I have done it both ways and not noticed a difference worth worrying about.
These are the two most common approaches to joining knitting in the round. Both methods work with every style of cast-on and with both circular needles and double-point needles. No matter how you join knitting in the round, at the end of your project, you will notice a slight jog on the bottom edge where the join occurred. As you weave in the end, you can cover that jog up a bit.
Now that you know how to join your knitting, what will be your first in the round project? For more great knitting tips check out the Knitter's Handbook on Craftsy.