If you have a septic tank, that may need cleaning out.
If it is the main drain in the house, there is usually a cleanout at the
farthest end of the drain, a plug that lets you feed an auger in without
going through any traps. You find this in the basement or crawlspace.
This would be work for a power auger, which can be rented for the job.
Electric augers are big with a lot of cable. If
augering the main drain in the house doesn't help, then augering the
drain from the house to the outside would be next. There is usually a
cleanout just below the point where the main drain leaves the house.
Remove the cap and start augering again. When using a power auger you
won't feel resistance when you get to the clog. You will hear the motor
start to slow, and that is when you need to reverse the motor and back
out, going back and forth till you cut through the clog. Be prepared,
this is a messy, smelly job.
If you have a septic tank, you can't tell if the drain
is clogged or if you need the tank pumped out, but the smart bet is the
tank will need cleaning first. If you have a drain going out to a
municipal sewer, you may want to check with neighbors to see if anyone
else is having trouble, it could be in the city's drains at the street.