Easy job. Try boiling water/Bleach and pushing a mop down there (if its a straight drop). Check there are no obvious blockages (food/hair/gravel/leaves etc)
If this fails, either buy some drain rods, or use a hose pipe and push it as far as you can (putting the hose on might help, or it might blast stinky water back in your face, your call with that one), if that doesn’t work, go to the road and find a drain cover by your house, open that up, identify the pipe leading to your house and try above, from that end. If that doesn’t shift it, then pay someone else to do it!