Help you with what?

Where are you stuck?

You do know how PWM allows a digital output to supply more or less power by varying the amount of time the pin is active?
For a single RGB LED, you can implement PWM using a dedicated PWM functionality in the chip. Or using hw timers. Or just pure software.

To change color "randomly", you can use a PC program to create an array of random numbers that you insert in your source code. The random numbers would represent the intensity of red, green and blue. Potentially also how long time until next color.

Then you can decide if the color should changed instantly, or if you should gradually change from one color to another.

The above would represent a quite simple program - each individual thing can be broken out and implemented/tested separately.