> logfile
or
cat /dev/null > logfile
if you want to be more eloquent, will empty logfile (actually they will truncate it to zero size).
You can also use
truncate logfile --size 0
to be perfectly explicit or, if you don’t want to,
rm logfile
(applications usually do recreate a logfile if it doesn’t exist already).
However, since logfiles are usually useful, you might want to compress and save a copy. While you could do that with your own script, it is a good idea to at least try using an existing working solution, in this case logrotate, which can do exactly that and is reasonably configurable.