These are the little one's socks, but the basics are the same for nearly all the socks I make. Since the littlest little has giant chubby toddler feet and yelled "NO LIKE IT! TOO TIGHT! NOT COZY!" on my first attempt of a sock, I bumped up the stitch count and did the cuff in 2x2 ribbing and carried it down the foot at well.
I prefer fingering weight yarn for socks that are meant to be worn with actual shoes, as anything thicker is too chunky. That said, I've made socks in bulky weight yarn that works out fine.
For these toddler size socks, I cast on 44 st,, divided them over three needles and worked 2x2 rib for a few inches (in this case 5 stripes worth). Adult sizes I usually cast on about 64 stitches, depending on the foot. I work my socks on size 0s or 1s, because I am a loose knitter and you want a firm sock fabric. Loose fabric shoes wear and holes and feels icky on the feet. Go for tight, and go down a needle size or three if you need to.
For adult socks, I'd generally do an inch or so of ribbing and then switch to stockinette or another stitch pattern. I kept the toddler ones in ribbing in case I was off on the sizing and needed the ribbing to suck in any excess.
Once the cuff is as long as you'd like it, take half the stitches (22) onto one needle, arranging the rib columns the way I liked them and worked the heel flap back and forth over those.
Now, over the years I've become picky about heel flaps. You work the heel flap back and forth across one needle, no longer in the round. The heel flap gets a good amount of wear, so I want them reinforced with a slip stitch pattern, but I hate the ridges that come with the standard K1, sl1 on the right side rows (plain ole purl the wrong sides) heel stitch pattern. And so I nearly always do eye of partridge instead, which is k1, sl1 on one right side row, then sl1, k1 on the next right side row. I find it makes for a slightly flatter fabric with all the cush as the regular heel stitch, and it also breaks up any pattern in self-striping/self-patterning yarn very attractively.
I also always keep 3 stitches in garter at the edges, as it helps me keep track of how many rows I've done so I can match the second sock, and it makes an attractive detail line on the finished sock. And of course, I slip the first stitch of every row as if to purl with the yarn in front so I have a neat, tight chained edge to pick up stitches after I turn my heel.
I work the heel flap until it's a little more than square--for grown ups about 2 1/4 ish inches, for the toddler sock about 1 1/4 inch--stopping after a right side row. Then I turn the heel. There are about a billion different ways to shape the heels, but my favorite is a round heel.
Pop a stitch marker in the middle of the stitches, marking the center of the heel flap. Purl across the heel flap stitches, until 2 stitches past the center, p2tog, p1, turn the work in the middle of the row. Slip the first stitch, knit until you are 2 stitches past the marker, SSK, k 1 and turn. Repeat the purl row, slipping the first stitch and purling to 1 stitch before the gap, p2tog across the gap, p1 and turn; knit across to 1 st before the gap, SSK across the gap, k1, turn. Keep doing this til all your heel flap stitches have been used up and worked. Voila, a heel!
Then I use a new needle to pick up one stitch per ridge along the side of the heel flap (see where that chained edge comes in handy?), plus 1 more stitch at the corner of the heel flap and instep stitches. Knit across the instep stitches in whatever stitch pattern you're doing--I like to knit all the instep stitches onto one needle. Then take another needle and pick up the same number of stitches along the other side of the heel flap, including that one extra in the corner. Use this same needle and knit across half the heel stitches. This is the new beginning of your round. Slip the other half of the heel stitches onto that needle holding the first side of the picked up heel flap stitches.
You should have three needles: Needle 1 holding half of the heel stitches plus your picked up gusset stitches, Needle 2 holding your instep stitches, and needle 3 holding the other side picked up gusset stitches and the other half of the heel stitches.
Then you start your gusset. Work one round even. On the second round, work the gusset stitches on needle 1 until you have 3 left: k2tog, k1. Work your instep stitches on needle 2. Then at needle 3, K1, SSK and work the rest of the gusset stitches. Work this decrease round every other round until you've decreased away the extra stitches you picked up from the heel flap and are back down to your original cast on number.
When I do socks for myself, I usually work the decrease round every round for a few times, then switch to every other round, just because of the shape of my foot. See what works for you.
Work the foot until it's about 2 1/2 inches shy of the total length of the foot (in the toddler's case: 1" shy). Then start the toe decreases to shape the toes. If you're doing adult socks, you'll wind up with about 20 stitches total for the toe. For the toddler ones, I decreased until there were 12 total stitches. Here's how to do 'em. Needle 1: k to the last 3 st, k2tog, k1. Needle 2: k1, ssk, k to the last three stitches, k2tog, k1. Needle 3: k1, ssk, k to the end. Repeat this decrease round every other round until you've decreased about half of the stitches you need to get rid of away. Then I like to switch to decreasing every round because I hate a too pointy toe.
Finally, you've gotten down to 5 stitches on each bottom-of-the-foot needle (1 and 3), and 10 on the instep needle. Work across those last 5 stitches on needle 1 using needle 3, so you now have 2 needles, each with 10 stitches on them and the working yarn is at one end. Now, break the yarn leaving a longish tail and kitchner stitch those toes together. It's not hard, it's just fiddly. Follow one of the zillion tutorials online and you will be fine. Don't over think your way into a problem. When you're done, admire your new sock and go make another one now before you forget.
Whenever I've taught folks how to knit socks, I've always told them not to think too hard about how to turn the heel or what you're doing until you've done it. This of course is the reverse of my normal knitting advice, but for socks, if you've never knit them, you'll read through the directions in the pattern and be like, THESE PEOPLE ARE NUTS THIS MAKES NO SENSE. Just trust in the pattern and you shall see!
The specifics of the toddler socks, written in my lazy girl shorthand:
co 44, 2x2 rib for 5 stripes.
heel flap 22 stitches, eye of partridge, 3 st in garter at each edge. Work for 18 ridges. Turn heel, (2 past center), pick up 20 st. Shift gusset decreases in to keep 2 st in purl at gusset edges to continue the 2x2 rib over instep. Dec e/o round til 44 st, work 45 rows from flap. Toe dec, e/o round until 16 st on instep, then every round til 8 on instep. Slip edge stitches over their neighbor (eliminates dog ears--I'm fussy), kitchner and weave in ends.