How to use Arduino to control a switch

I was wondering if it was possible to use Arduino to control switching on/off an LED strip that's powered by another source and also control its brightness. Most of the other examples I've found online require opto-isolators and things like that, just wondering if there is another way to do it without them. Thanks!

I've got a similar challenge: using the arduino to control a switch connected to outside power.
For a school demonstration project, I have an Arduino Uno R3, a 24AC solenoid valve, and a Songle power relay 5V DC Dual Power Relay Module (SRD-05VDC-SL-C). I want to use the arduino to send an open/shut command to the valve to water a plant. The Arduino gets its 5 volts of power through a USB cable to a computer, but the valve is 24volts, alternating current, thus the power relay module. But the solenoid also needs an outside power source, right? If i wire the arduino to the power relay module, and then complete a circuit between the songle, solenoid and public power (220 volts), will it fry the arduino? Do I need some other hardware, or just some guidance in wiring this properly? Thanks!

just wondering if there is another way to do it without them

There is tutorial, using MOSFET's: