It's much harder to make a trade after the non-waiver deadline, but it can and does still happen. First, step to make a trade is to place a them on revocable waivers. Revocable waivers means that at any time the team can pull them back and not lose that player. Once a player is on waivers teams can put a claim in on him. If multiple teams place a claim then priority is first given to the lowest ranked team in the same league as the one the player is in and then the lowest ranked team in the other league. After a player has been claimed there a few options. The team that placed that player on waivers can pull him back, they can negotiate with the highest priority team that filed a claim to work out a trade or they can just let the player go. If a deal is going to be worked out for a trade the two teams have two days to make it happen. If a player goes unclaimed for two days then the team is free to trade him to whoever they wish.
Being claimed off waivers is not the hardest part of getting a deal done in August. You have to remember that the only players that can be traded are players who have cleared waivers or players not on the 40-man roster. So, for a deal to get done the team giving up the major league talent has to get back a prospect that they feel will be worth making a trade for that is not on a 40-man roster.
Even though it is no where near as fun as the non-waiver trade deadline, trading in August can still be exciting. Best part about it is that it is very secretive when it comes to who has been put on waivers so we as the public may never know how close our favorite over priced star came to being traded in August.