Create an account at http://www.worldoflogs.com/
From there, you will have a client link at the top right. Make sure that when you click that, you have the java tool pop up with three client options.
Now, you are ready. In game, type /combatlog into the chat window. You should get feedback indicating that the combat logs are being recorded at xxxx\xxxx\combatlog.txt. Where the x's are will be folders on your computer which just depend on your version of OS, etc.
The client options for uploading will include a live update option where it will upload each fight as combat ends. That one usually is the hardest to get through many computer's security and might be more hassle than it's worth but you can try and see. Another option will be to manually upload the logs. If you choose that one, once you click the upload you will get the option to browse to the combatlog.txt. Just remember the xxxx\xxxxx\combatlog.txt message you received earlier and go there.
The live option you would want to start before any fights. The manually upload would be done after the fights. The /combatlog needs to be typed before the fights and then again to turn it off when you want to stop recording the combatlog.
"he doens't need healing, he doesn't need healing, he doesn't nee-WHAOSHIT!wtf was that man!". Please stop leaning on TDR. -Teng