Note: As of version 8 this method is deprecated and no longer recommended. A much better option is to use the new live api via Geocaching.com access=>Publish logs
GSAK allows you to key your cache log information offline, then help you to log this information online. Note: When using this feature you must make sure that you have manually logged into GC.com with your Groundspeak user name and password. This is how gc.com know exactly who you are when the logging is done.
If you look at the add/change notes screen you will notice it is split into 2 sections. There is also a button that says "log cache". For the new/novice user, all you have to do is enter the details in the log section, then click on the "log cache" button. This will open up the log page for this cache, now just paste the contents of the clipboard (Ctrl-V) into the comments section. This can be done when entering the details or at a later time.
All this button actually does is run the macro called "LogCache.txt" which is now installed into the "Macro" folder of the install folder of GSAK. The default actions for this macro is to just call up the corresponding gc.com log page and copy the contents of the log information to the clipboard. Note the default URL used is Geocaching.com because the majority of GSAK users are with them. However, If you use another provider, it is just a matter of editing the macro URL to change this behaviour.
Advanced users can just edit this macro and change it to how you would like this to work. However, I suspect advanced users may even just ignore this button and macro and make up their own. That way they can add a button on the tool bar that calls up their own version of this macro.
My interpretation of how this would work for the average advanced cacher that likes to go caching, update logs in GSAK offline, then at a later date go online and update gc.com:
1. Set up your own version of the "CacheLog.txt" macro if the current one does not meet your requirements
2. Add a macro button to the tool bar for this macro
3. Go caching
4. Update all your days/weeks caching offline in the GSAK logs (perhaps also update your finds and found by me dates at the same time)
5. When you are ready to go online and update gc.com with your GSAK offline logs, set a filter that reflects all the cache logs you just updated (perhaps using the found by me date)
6. Click on your macro button for each waypoint in this subset. This will call up the gc.com log page for that cache, then all you need to do is paste (Ctrl-V) to copy the GSAK log into the gc.com log area. By doing it this way you get to select the log type, date, coordinates, etc before actually making the post to gc.com
I suspect you will have your own variations of the above steps, but I hope this will at least give you something to start with.