What happens to a Pokemon's stats when evolved?

Here's my question.I want to know what happens to a pokemon's stats when evolved. For example, let's say I use a fire stone on Vulpix. As it evolves into Ninetales, do its stats change? Or, if I trade Kadabra, and it evolves into Alakazam, do its stats change?Basically, does the act of evolution boost stats at all?

Yes, that's one of the whole points of doing that, besides having access to newer moves.
It takes the base stats from a Ninetales, and not a Vulpix when it is evolved.Not Fully Evolved pokemon generally have much lower base stats compared to their end products.

But do the stats change the moment you evolve it, or do you have to level up first?Say that Vulpix's stats are this:
HP: 31
Atk: 34
Def: 23
Sp. Atk: 40
Sp. Def:36
Speed: 40Then I use a fire stone.
What happens to those stats now?

Can't answer that question unless I know the EVs invested and IVs, as well as Nature.Look at the base stats between the two.
http://www.smogon.com/dp/pokemon/vulpix
http://www.smogon.com/dp/pokemon/ninetales