Besides long-tailed cast-on, there are other, more elegant, more confusing ways of casting on for knitting.
More cast-ons similar to long-tailed cast-on: The old Norwegian cast-on. It’s a good cast-on for socks, as it’s stretchier than a long-tailed.
Here’s a nice video showing casting on of knit stitches in the Twisted German technique.
You can do an alternating knit and purl cast-on, also called German Twisted. It’s very stretchy for socks.
Knit and purl cast-on
Finally, there’s Judy’s magic cast-on for toe-up socks.