Personally, I never seem to be able to master the long-tail method of casting on – the one that is wrapped around the thumb and index finger in a Y-shape. I have my own method that I’ve done forever, yet never have seen duplicated on YouTube. I wrap the yarn on my left thumb, and knit a stitch with the needle in my right hand – this is my version of the long-tail. And it is very nice and stretchy. However, the cast-on by Alasdair Post-Quinn made the Y-shaped long-tail cast-on sensible because of the two different colors being used. I may actually be able to do it now!
Given this, I know that I have found a lot of videos on YouTube for casting on before knitting. Being somewhat encyclopedic in my approach to things, I decided that this post would be a collection of the different ones on YouTube I found to be especially useful.
Traditional Long Tail Cast-On
Long Tail Tubular Cast-On for 1×1 and 2×2 Ribbing by Ysolda Teague
Stretchy Knitted Cast-On Using a Crochet Hook from the Scarlet Zebra
Estonian Cast-On for Knitting Socks with Nancy Bush
Channel Island Cast-On by Oftroy
Double Knitting Cast-On with Alasdair Post-Quinn
German Twisted Cast-On with Lucy Neatby
And these are just a few! In particular, I highly recommend that you connect with Oftroy on YouTube. She has oodles of videos about cast-ons and different ways to do it – braided, multi-colored, whatever – and her videos are very watchable. She blogs here. Lucy Neatby’s YouTube channel has some unusual videos, such as on knitting based on Navajo plying (used in spinning), and a very tidy bobble. She is not a prolific video-maker, but her stuff is very clear and solid.
What would we do without the internet and YouTube??? There is sooooooo much to learn and share!
Ink, Yarn & Beer 
Not everything on YooToob is right; some are purposely wrong!
The long-tail cast-on method is for Continental knitters. You can do the left-thumb-and-knit-with-right-hand for the English method… both are exactly the same! Don’t make it more complicated than it needs to be.