My board is USB powered. How do I use this for other circuits

Hello, everybody and thanks for the help

I have been working with 5V and 3.3V PICs that I power from the power outlet on the wall (with a device of course to change AC into DC). Once I also power my small circuit from the USB.

My question is, now I want to use micros other than PICs. For example the Stellaris Lauchpad or the STM32 Nucleo. Now these boards are USB powered, meaning I connect a cable to the PC through a USB cable and I can say turn on and off a LED.

Well that is well and fine but what if I want to implement non-trivial circuits with these boards? Say (DC, stepper) motors, PWM, LCDs, etc. or maybe if I have to use (in the case of motors for example) 12V or 24 V to power that part of the circuit. What do I do? I mean I am guessing that the ground part of the USB power and the ground part of say the motor control circuit should be the same right?

I would very much appreciate if someone can explain this to me in simple terms, perhaps an example...

Thank you very much.

I use a ("USB charger" thing like my cell phone uses), to power the micro-computer.
THEN
I use a large "wall wort" (same as above but 4x bitter in size) that outputs 24 volts and up to 4 amps, to power motors.
YES
The grounds need to connect together.

I'm only repeating what ronsimpson already have said, you can connect anything together as long as you common the grounds first (and don't start a fire).
The only thing you can't connect is an old British car wired with positive earth.