Oh my goodness the Long Tail Cast On. I use this almost every time I cast on a knit project. Back when I was a newbie knitter I remembered always being afraid of this technique. It looked intimidating watching others do it, I was afraid my work would unravel, I could never seem to measure out my yarn well enough or get my stitches to look all even. I tried it out a few times then but just never used it. However since I'm kind of a perfectionist a main focus of my designs has always been to achieve the best finished piece. So let's just say I think I've tried like every cast on there is up to this point and I just didn't care for the look and feel of any of them quite so much as this one so I thought I'd give it another chance. It took some practice but if you just take it slow, you'll get it. It really does make that edge much nicer and for pieces that need a good stretchy edge like hats and boot cuffs it makes a world of difference! Here is a great tutorial on how to do the basic long tail cast on done by We Are Knitters, if you don't like the idea of starting without a slip knot like shown then follow the same directions just begin with a slip knot on your hook until you feel more comfortable.
The corresponding bind off that I like to use when using the Long Tail CO is called the Sewn BO or sometimes called the long tail BO, there are a few different ways I've seen to do this one but I like Elizabeth Zimmerman's the best. Happy knitting!