I personally would prefer to have a child table with related records in this case (rather than appending info onto a single field). You could then view your activity chain through a portal and get the same result without having to click the button.
If you must append (can't figure out how this would be a must):
SetVariable ($Task; Table1::Tasks)
SetField (Table1::Tasks; $Task & Get(CurrentTimeStamp) & Task Entry)
Setfield (Table1::TaskEntry ; "" ) /##clears out the task entry field in case you doubleclick the button by accident
You could really do it in a single self referencing Setfield, but I shy away from self referencing functions as a matter of course...got myself into trouble too often with them.
SetField (Table1::Tasks ; Table1::Tasks & Get(CurrentTimeStamp) & Task Entry)
Hope this helps...especially if you choose the Child table route :)