With a short sale house, you are dealing with the seller first. You negotiate an offer just like you would with any other non distressed home. The house is usually listed at market value (price that other homes in similar condition, size and location are selling for). The seller owes more to the bank than what the current market value of the home is. Once a seller accepts the offer they go to their mortgage holder and negotiate with them to accept this offer and forgive the difference that is owed on the house.
The banks are looking for the highest and best offers. Once a seller presents the bank with an accepted offer (one the home owner has accepted) the bank can then approve the short sale, counter the offer or reject the offer. The bank should be dealing with one accepted offer at a time, but every situation is different and banks seem to not be playing by the rules lately.
The process can take awhile to get an answer back from the bank. If your offer was countered by the bank you would still be in the running. If the offer is rejected, then there may very well be another offer on the table by someone else. You would have to check with the listing agent to see if they are working with another offer at that time. If they are, then you would have to wait to see how that offer plays out. If not then you can resubmit a new offer. This is part of the reason why the process takes a long time. Another reason is that the banks don't have enough people to process short sales so you have to be patient.
The best thing to do is make your offer the best you can right from the start. A short sale is a bit different to pursue than a regular transaction. Just because the seller accepts your offer doesn't mean that you have a deal. The bank has the final approval. What may look good to the seller may not look good to the bank. If you are in a hurry or pressed for time, a short sale may not be the way to go. If you have time, it could be worth the wait. Best of luck.