a real basic one would be
$ echo `date`": what I'm doing now" >> timelog.txt
If you want to process it later, it's easier if you make that date +%s
or date +%F%T
.
You could wrap that as a shell script:
#!/usr/bin/bash -
echo `date +%s` $* >> ~/timelog.txt
Some hint of what you really want to do might help.