Systems are not all the same but you can apply some logic to this.
The toilet discharges into a 3" (occasionally 4") line.
Smaller lines (sink and tub) connect to that line.
The sink drains, maybe because it is higher than the shower and there is enough volume in the line that it doesn't back. If you put a lot of water into the sink it might back up into the shower, but the information probably doesn't change what you will do.
If everything else in the house works ok, such as other toilets, then the plug is probably not far away.
If you have a convenient cleanout on that 3" line near the toilet you could use that to run a big snake down it.
If there is no cleanout that will clear that line, then remove the toilet and run the biggest snake you want to invest in down that line. Get a new wax ring while you are shopping for the snake. If it is a very old installation, get a new set of closet bolts.
You might try a garden hose with a short, straight nozzle (not one of those lever things), push it down with the nozzle set in jet mode. You should get a hose with the shiny plastic outside rather than the soft rubber, because it will be easier to push. It will also be easier to push when the pressure is in the hose. sBe sure there is a handy place to turn off the water in case you start to make a messy flood.
But if it's plugged because someone flushed a T-shirt down the toilet, forcing it down with water might make it worse.
After you get it unplugged and before you pull the snake or hose out, use another length of hose to wash things down so the hose or snake won't be so messy when you pull it back.
If all this sounds too tough, call a plumber, after you read the thread on what it costs to hire it done.
