Step 1. Google 'Brand name twitter account'.
Chances are, if said brand have an account, Google will know it, and display it... For those of you not familiar with Twitter ID's, they all start with an '@' symbol. For example, mine is @Lynden2883
Step 2. Tweet Your Disgust.
Create a Tweet, this doesn't have to be Shakespeare's greatest work, and remember you only have 140 characters (including spaces), and you HAVE to get the Twitter ID in there too (maybe even a hash-tag). Make it simple, and make it instant. It's no good waiting until you have calmed down, it has to be there and then.
e.g. Really p*ssed off with @BrandName today, completely #RuinedMyDay, #Thanks
Step 3. Wait For A Reply.
If said brand have a Social Media team worth their salt, they should get back to you, and usually within a couple of hours. In both my cases, it has been within minutes. After all, that's what they are paid to do.
Step 4. Be Brazen.
My Mum always told me, "If you don't ask, you don't get"... so be brazen. Once they've replied, tell them what would make it better, what would be ample compensation for your miss-fortune / inconvenience. Don't ask for something that's clearly not going to happen, like the winning lottery ticket, or £500. But something realistic that you know should be well within their power.
Step 5. Show Gratitude...
This is something I think people often forget. We are all too quick to complain when things go wrong, but not so quick to give praise when something is handled right. OK, so they messed your order up, or ruined your day, but this wasn't the fault of the customer care / social media team who handled your enquiry, so show a little gratitude in the way they handled it. Sometimes a simple 'Received #GreatCustomerService from @BrandName today, #Thanks :)' goes a long way, and will ensure that team, keeps working the way they did. :)
1 important thing to remember... 'The World Is Watching'. Whether someone follows you or not, there is a high chance that other people will see your tweets, especially if you are using hash tags in there too, and the brands know this also. So they want to be fast, they want to handle your problem, and most importantly, they want to be seen doing so. So use this to your ADVANTAGE!!!
Go on. Embrace the Power Of Social Media!