how does redshift prove expansion is accelerating?
You're right, a redshift will give you a measure of a velocity, not an acceleration. I'm assuming when you say acceleration, you're referring to the accelerating expansion of the universe so you're not looking at the particular acceleration of an object (which you could get from examining the force of gravity imparted on that object). 

So in addition to a redshift, you need to find a way to independently measure the distance. To get out to an appreciable redshift (z~0.5), Type Ia supernova are used as "standard candles". They are considered standard because they're believed to be from white dwarfs that explode because they have reached their maximum possible mass, the Chandrasekhar limit, of 1.4 solar masses. Therefore, when they explode, they should all look about the same and any difference in brightness would be from how far they are away from us. So they measured the distance and the redshift of the galaxy the supernova originated from to determine the expansion of the universe appears to be accelerating over time.