My go-to cast on for knitting is the cable cast on. It’s simple to do and produces an even, sturdy stitch for perfect edges that don’t need to stretch too much.
1) How to cable cast-on: Start with a slip-knot on the left needle.
2) Knit into the slip-knot.
3) Transfer the stitch from the right needle to the left needle knitwise.
4) Insert your needle between the two stitches on the left needle.
5) Knit the stitch, and transfer it to the left needle knitwise. Continue in this pattern, knitting between the last two stitches on the left needle and transferring the new stitch to the left needle knitwise, until you have cast on the correct number of stitches.
If you are casting on a ribbed edge that doesn’t need to stretch a whole lot (like the bottom of a sweater), you can modify the Cable Cast-On to be an Alternating Cable Cast-On. It starts the same as the cable cast-on. You make a slip-knot on the left needle, knit into it, and transfer the stitch knitwise to the left needle (as steps 1-3 above).
4) To make the purl stitch, you insert your right needle between the two stitches from back to front.
5) Wrap the yarn around the needle as if to purl (shown here from the bottom)
6) Pull the stitch through to the back and then transfer the stitch from the right needle to the left needle knitwise. Continue your cast-on process, alternating between knitted cast-ons and purled cast-ons (for a K1 P1 rib. You can use the same knits and purls in different orders to make any variety of ribbing. For example, 2 purls and 2 knits make K2 P2 ribbing, 2 purls and then 3 knits would make K3 P2 ribbing, and so on).
If you’re a bit confused about what it means to slip knitwise, don’t worry! The animated image above shows you how to slip a stitch knitwise. Basically, you insert the needle into the stitch from front to back, like you would if you were going to knit the stitch, and then move it to the right needle without actually knitting it.