Animations are quite simple, you firstly need to create a full Skelton with all the bones. Ie right hand bone, elbow, head, torso etc etc. Then you apply the vertexes to a specific bone. After that you can select the bone and rotate or play around with it and the vertexes that are apart of that bone will move along with it. It takes abit of playing around with to get used to it.
Anyway Im on my laptop at the moment, but I will go onto my modelling computer

and will guide you through it if needs be. (I cannot remember all the function names off the top of my head but I know how to do it)
Ps. you may need to change the weight, try 0.5 or is it 1.0? To be honest its been a long time since ive done any animations but from what I can see the main problem your having there maybe from the set weight.