Your focus indicates a sewer issue and not a drain issue.
The first challenge is to determine which branch leg of the sewer is the issue and then assess where all your access ports are. Sometimes an outside access port has been covered over by dirt/mulch etc.
If you know where the blockage is ... then as mentioned by other contributors ... you will need a snake. They can be hand driven or motor driven. For great access to the blockage you may need to remove the closest toilet, since snaking through the lower S trap of the toilet really inhibits the snake's effectiveness. Depending on how your house is built ... the roof sewer vent pipes can be a good access point (and sometimes that is where the debris has gotten into your sewer if you have overhanging trees). I have had success with running a garden house up to the roof and down through the vent pipe. You need to have a second person watching by the the toilet to make sure it does not back flow on to the floor. You can get hose spray attachments which help propel the hose and add turbulence to break the blockage ... but I have never tried them.
If your blockage is recurring over the seasons ... and if you have a number of trees close to your sewer line outside then you can have tree root intrusion into the sewer. In that case you need a professional with a special snake that actually has cutting capability to remove the roots.
Attached are 3 photos ... manual snake, motor snake, hose spray nozzle
Good luck with your troubleshooting!