blur background of video to finish with logo in front

Its very simple.  Apply a blur effect to the video layer you want to blur and set 2 keyframes to bring the blur radius up.

At the same time keyframe the opacity of your layer with the transparency (which is obviously above the video layer) from 0 to 100.

It doesn't get any more basic than this.  you're talking about two layers, 4 keyframes & a single blur effect.

A person who's followed one single "Introduction to After Effects"  tutorial would be able to pull this off in less than 30 seconds.

Hi,

Here is a video tutorial link for After Effects. The voice in the tutorial videos is Japanese. But you may be able to understand them even if you just watch the video only.

https://www.youtube.com/user/DENPOZI

Thanks,

To rephrase Dave LaRonde's answer:

Yes, it is very possible using basic AE tools.

AE is not easy to learn quickly, so be prepared to put in many hours of studying to be able to use AE.

Oh, you're the lady who wants to get rid of a logo on a piece of paper.  I get the feeling you're REALLY new to AE.  Here's an analogy:

Learning to use a video editing application like Premiere Pro -- or any good editing app -- is like learning to drive the family car.

Learning to use After Effects is like learning to fly the F-22 Raptor stealth fighter.

You really have to know the basics in AE or you'll get hopelessly lost.  You need to learn its arcane terminology, too.  Almost everyone in the forums uses it.  Those who don't have a tough time.  So while it's tempting to jump into the deep end of the pool with AE, don't do it wearing lead weights.  Learn the basics.  You'll probably be surprised at the weird way AE does things, and you'll be glad you took the time to learn.  Here's some help:

After Effects tutorials | Learn how to use After Effects CC

Good luck.  It's confusing at first, but you'll get the hang of it.