Cirkit Designer will autoroute the wires in your circuit. You have a few ways to access this feature.
Right click on the canvas and select Autoroute All Wires to autoroute all of the wires in your circuit
Right click on a component and select Autoroute Component Wires to autoroute all of the wires connected to that component
Right click on a breadboard and select Autoroute Breadboard Wires to autoroute all of the wires connected to that breadboard
After wiring up your circuit, you may find that you want to reposition a component, including any wires connected to that component.
To enable wire-following, either hold down the shift key and then click and drag a component, or click to enable the feature from the Power User Features dropdown.
Now, let's reposition the pushbutton. We see that the wires connected to the pushbutton automatically follow the component!