You make an offer just like you would any regular transaction. There may be addendums that need to be included with your offer. Short sales will be subject to bank approval.
With a short sale you are dealing with the current owner first, not the bank. The current owner tries to sell the property for market value. Once they have an accepted offer they will take it to the bank for approval. The bank can accept, counter offer or deny the offer. It could be several months before you hear back from the bank. It will depend on the bank and how many short sales they are dealing with.
Foreclosures are already bank owned to you are dealing directly with the bank. It can go a little quicker, but again it will depend on the bank and the amount of foreclosures they have.
Once the bank accepts the offer they will give you a closing date. You need to be ready to go, the banks don't like delays once the deal is ready to close.