That looks like heavily blurred footage of some lights blended with a still image using a blending mode.
So, import a still image, make a composition based on it, import a video with some colored lights moving around, make a layer in the same composition based on this footage, apply a blur effect to the lights layer, and then use a blending mode to blend the two layers together.
If that didn't make sense to you, then start here to learn After Effects:
That's a fairly vague request. You could be talking about the fake light leaks as Todd suggests, OR you could be talking about the logo with the transparent letters in the center OR you could be talking about the animated lower-third in the left corner.
In any case, Todde's absolutely, positively correct about learning AE from the ground up. The excuse that you "only need to know a few things and that's it" doesn't fly, and it never has with AE. Furthermore, it would take too many flippin' emails to teach anyone the techniques necessary because you don't know the arcane AE lingo.
Here, I'll toss out just a few AE terms germaine to making that video: track mattes, creating shapes, masking solids, text layers creating an alpha channel, keyframing position, using easy ease keyframes, parenting.... are you catchin' my drift?
Do yourself a favor -- use that link Todd supplied.