PWM is mostly used in controlling motors, fans, dimming LEDs and other areas where variable analog voltage is required from digital electronics. By changing signal duty cycle you can control average voltage level and thus drive devices as you would change supply voltage. In order to get PWM signals simplest way is to build a 555 timer based circuit. Zak made an Attiny25 based PWM controller (actually two versions) where PWM duty cycle and so fan speed can be controller with two push buttons or potentiometer.
PWM signal drives MOSFET transistor that can drive higher loads. Particular STP36NF06L is capable of driving 8A load current. If you need more, then couple parallel MOSFETs with heatsinks should do the business.
We recommend EasyEDA for circuit design and PCB prototype