A while black I uploaded a video on my YouTube Channel, showing how to knit the easiest socks. In the video tutorial I explain the technique, however, I was asked to write it all down in sizes. The interesting thing about this pattern is that you can adjust it according to your foot length.
Now, for kids, let's say 3-4 years old, I would cast on 32, work in the round for a few inches, however long you want the cuff to be, then knit the colour contrast yarn in and knit the foot. At this point you can measure it, making sure you leave an inch to shape the toe.
For older children, 5-6 years old, I'd cast on 36 sts and work it exactly as the video shows you.
Then for +7 years old, you'll be ok to cast on 40sts. The same works for ladies small, and then for men, you should cast on 44sts small and 48 sts large.
I need to specify that all these instructions are for worsted weight yarn worked with 4mm needles. You can use DPNs and knit one sock at a time, or magic loop method and work 1 socks at a time or, be brave, and do two at a time. 😊
I hope this was helpful, please use my video tutorial for guidance, don't forget to subscribe!