You have to visit the test center where you took the test and submit your TRF back to them. They will make you fill out a form and then you just have to make the payment.
I had my IELTS writing result re-evaluated last month. My score went up from 6.5 to 7 and it took around 4 weeks for the re-evaluation to be completed. I was sure that I deserved at least 7, that's why I went straight for re-evaluation. If you are sure that you did well in the test, you should go for it. Good luck!