cat /dev/null > logfile
if you want to be more eloquent, will empty
logfile (actually they will truncate it to zero size). If you want to know how long it "takes", you may use
dd if=/dev/null of=logfile
(which is the same as
dd if=/dev/null > logfile, by the way)
You can also use
truncate logfile --size 0
to be perfectly explicit or, if you don't want to,
(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.