I went through the pain of buying a short-sale house about three years ago. It might not have been as serious a short-sale as some of the others discussed above, but since you’re looking for information…
I was shopping around for a house, and the realtor I was using showed me this one. I really liked the layout and the neighborhood, and the price was in the range of what I was looking for (~180-220k). I decided to put in an offer of 200k, and it got accepted.
Then the pain started. The couple who owned the house was apparently in a bad spot. They had bought the house about 9 months previously. It was never explicitly said (since I think it’d be technically illegal), but from what tidbits of information were mentioned in passing, I’m guessing they did a “no money down, all costs rolled into the mortgage” deal. So they were starting out in the hole, and hadn’t had much time to work the principle down. Then they got pregnant, and he lost his job. They had missed 3-5 months of payments, so nothing going to the bank, plus late fees etc continuing to bump up the loan amount. I’m guessing they just wanted out.
They accepted my offer (and $2000 earnest money) at the end of April. Final closing wasn’t until early July. So there was roughly 2 months of checking with the realtors trying to find out if the mortgage holder was willing to sell or they’d just foreclose.
Things were a little panicy for me during the last month. I had been living in an apartment, and had not renewed my lease (ending in May), and told the complex I wanted to go month-to-month after that. A few weeks later (early June), I got a “yes, they’re going to go through with the sale” call, and told the apartment complex that I’ll be moving out at the end of June. Then a week or so later I got another “no, they’re still running numbers” call, and I rushed back to the management office to let them know I still needed a place to live. Unfortunately, in that time they had accepted a new tenant in my apartment starting July 20th or so. They were willing to let me stay until about the 18th (since they needed time to do the outgoing inspection, steam carpets, repaint, etc), but after that I needed to be gone.
Needless to say, with that kind of a deadline, I was praying for a quick resolution on the sale. It got to the point where I was looking around for storage options and friends to crash with if it ended up I’d have to move out of my apartment before being able to move into the house.
Fortunately, one more call set the closing date for the first week of July. I went in, signed a bunch of paperwork, gave them the certified check for the down payment / closing costs, and had a house to move into with a week or so to spare. 
After all that, I’d say that an offer on a house should take into account market price, comps, etc regardless of whether it’s a short sell or not. The owner may want to get out of a short-sale situation with whatever they can get, but their bank is going to be comparing your offer to the current mortgage, and would probably be more likely to go along with the sale if they’re losses are minimized.