If you happen to find someone else's check you should look on the check and see if there's a number to call either the bank that issued the check or see if there's a phone number to contact the person who wrote the check.
If not I would recommend either destroying the check or returning it to the person who's name is on the check if possible.
On the check there should be the name of the person who wrote the check and the persons address where you could mail the check back to them.
Personally If I couldn't find a phone number or wasn't near the bank I would get an envelope and a cheap stamp, insert the check into the envelope and write a little note stating that I'm returning the check to them because I found it and the person lost it.
That would at least let the person know what happened to the check so they wouldn't have to worry.
The person who wrote the check likely has put a stop on the check anyway if the person who it was written out to has reported the check lost.
So it's up to you to either send it back to the check writer or just shred it up or return it to the bank listed on the check.