Most toilet clogs are cleared in under 10 minutes with the right tools and a little patience. You don't need a plumber for this.
Squeeze a generous amount of dish soap into the bowl. Follow with a bucket of hot tap water. Let sit for 5 minutes — this sometimes clears a soft clog entirely.
Insert the flange plunger with the flap sealed inside the drain opening. Push down slowly to release air, then plunge with firm up-and-down strokes. Ten to fifteen strokes is usually enough.
If plunging doesn't work, feed the toilet auger into the drain opening and crank clockwise as you push through the trap. Work it back and forth to break up or hook the clog.
If the toilet backs up repeatedly or if multiple drains in the house are slow simultaneously, the blockage is deeper in the main line.