In order to upload to WildStar Logs, you need to install a client application.
The WildStar Logs Uploader uses Adobe AIR. You can get Adobe AIR from Adobe's Web Site.
Once you have Adobe AIR installed, you can download the client here.
After installing the client uploader, you must then install the WildStarLogger add-on. Since WildStar does not have built-in combat logging to a file, this add-on handles capturing the combat events in-game and delivering them to the listening client uploader application.
You can download the WildStarLogger from Curse:
Note that the add-on and client uploader are often going to update at the same time, so if you see the client uploader auto-update itself for example, you'll know that you should probably check for a new version of the add-on as well.
The WildStar game does not support combat logging to an external file, so this means we have to do it ourselves. This is accomplished by using both the application and the add-on that you just downloaded. The add-on, when logging is enabled, will begin sending events to the system clipboard. The client uploader application can then be set to watch the clipboard and store the results in a WildStarCombatLog.txt file.
To enable the add-on, simply type /wsl from your chat window. This command will toggle logging on and off.
Once the add-on is sending events, you then need to set up the client uploader to receive events, and you need to tell it where you would like the file to be saved. That is done by filling out the top part of the client uploader window and hitting Start to begin listening for events from the add-on. When you no longer want events to be written to a file, you can hit Stop.
Once you are generating a WildStarCombatLog.txt file, you have two options for what to do with it. You can either upload the entire file at once, or you can enable live logging. In live logging mode, the client will upload fights as they get added to the file. This is ideal when you are progressing on a boss and want to study what went wrong in between each pull.
Regardless of which option you pick, you need to create a report to hold the log file. A report can either be placed in your guild or in your own personal logs. You can also enter a description for the report, although WildStar Logs will fill this in for you automatically if it recognizes the raid you've uploaded.
Reports can be Private or Public, and you can choose this when creating them. A public report can be viewed by anyone. A private report can only be viewed by members of your guild (or only by you if it is a personal log).
To upload an entire file at once, select it using the file picker next to the Upload button and then click Upload.
To enable live logging, simply click the Start button next to Start A Live Logging Session. This will always use the WildStarCombatLog.txt file found in the folder you picked when connecting the client to the add-on.