First off let me start by saying I will only beta a story that I want to beta. Just because you are asking does not mean I will. If the story has no interest to me then I will have no interest in correcting it.
I was taught grammar by one of the strictest teachers ever. I know what punctuations go where, how to brighten up a bland sentence and how to spell even the most unheard of or complicated words. If you want your story to be completely torn apart limb from limb, but improved a thousand times over, you may come to be. Do keep in mind I'm very strict about grammar, and I will find any and every error in your writing; however, I will also be sure that your story flows to its fullest potential.
I will not read your story as a whole until every nook and cranny of it is emptied and corrected from its pieces of grammatical and spelling error dust bunnies. A story that has many errors turns me off from it really quickly, and I often find myself trying to fix it without even the individuals permission if I find the plot to be entertaining enough.
After corrections are made, I will go back and re-read. Re-reading ones story is one of the most important keys to a successful writer. Chances are I will re-read the story or chapter until I can recite it word for word. This is to be sure that I have not missed any mistakes; for we are all human, and we of course all make mistakes; however, it is my intention to see that no story I beta has one single mistake.
Re-reading the story will also help be sure there is a flow to it. To get an accurate feel of the flow in a story, I often read it aloud. Some may find this funny, and the members of my house hold I'm sure will get overly sickened by hearing me read aloud so much, but I feel it is the best way. It also helps to double, triple, quadruple check on any errors.