what actually happens when a bank goes bust?

Quick answer (for an investment bank): They try and "net out" as many positions as possible between the different counterparties. In other words they get together all the market participants who had deals with the bank and try and work out situations where they can deal with each other to try and cancel out as many of the positions as possible. Say Bank A had a contract with Bank B to sell 50 units of something at a fixed date. Say Bank A also had a contract with Bank C to buy 40 units of the same something at a fixed date. Bank A goes bust, so they get Bank B and C together and match them up so that Bank C "changes" which Bank it was going to sell those units to and Bank B changes which Bank it was going to buy 40 units from. This kind of matching up (it takes ages to work out for a big investment bank because of all the possible combinations) can solve most of the positions without causing too much disruption.

What's left over needs to be dealt with differently, I'm not 100% sure how they're going to approach it to be honest. It's going to take months, possibly even years, to fully unravel the mess on this one.