Oh, I've been there. Long tail cast-ons are frustrating until you have that beautiful moment where it makes sense.
What I would do is put the needles down
and watch the video. Break it down into individual steps, watch them a few times and then move on to the next part.
I'll try to explain it in the way I understand it:
1. Pull out the length of yarn you need (I normally do one foot of yarn for every twenty stitches I need to cast on). Let the tail end (the end you just pulled) dangle over your thumb. Let the end attached to the skein hang over your index finger.
2. Snatch the two ends that are dangling with the rest of your fingers. Spread your thumb and index finger a bit to make it taut.
3. Place the tip of your needle under the stretched yarn in between your thumb and index finger. Place your right index finger over the yarn and pull down.
4. Pull down enough so that it appears you have a loop on your thumb (and an open loop on your index finger).
5. See that thumb loop? Slide your needle up along your thumb, heading towards your index finger.
6. Here's the part that confused the crap out of me. You see that piece of yarn right in front
of your index finger? You want to slip your needle so that piece of yarn is going over
7. To this part, I'm sure you got it. Now what to do you do with that yarn you just put under the needle? Look at your thumb. You should still have a loop there. Bring your needle through
that loop, and then duck your thumb out of that loop.
8. Pull gently to tighten it around the needle. There! Long tail cast-on!
I had to sit for a little while and keep trying this until it clicked with me. I also kept playing the video, listening to Amy talk me through it while I was attempting it. It will make sense and then you won't want to cast on any other way (at least, I haven't.
Hope this helps!