Sollys right, don't want to dissect too much... theres always things to focus on though.
Heres what I do, it may or may not help you:
I start with placing my feet about shoulder width apart, and the bar should "cut" them into two equal halfs, one half in front of the bar, one half behind the bar. I bend at the hips and get my grip tight, then lower at the hips. At this point your shins should be comfortably touching the bar, back straight, chest out, head up. From your video, your start looks pretty good!
Squeeze your whole body... engage your lats, core, hamstrings, forearms, grip. Then starting at the hips, try and drive your heels into the ground as you "stand up" with the bar. It should stay tight to your body throughout the lift. When you reach lockout at the top, try and squeeze your shoulder blades together, really getting that tension throughout the back. On the way down, make sure you start to "sit" back down with your hips first with a slight bend in the knees, once the bar has travelled past the knees they can bend all the way back down until weight is on the floor.
Two standouts from the video was the issue b_cyrus mentioned, where your hips come up but nothing else does. And just be careful when lowering the weight back down, don't bend your knees too much initially or the bar will hit them.
As far as being sore, the more you deadlift the less sore you will get. Theres a big difference between an injury pain and general soreness though, however usually you'd feel the injury in the gym once it happened, not all of a sudden the day after (sounds like DOMS)