There are a fair few projects and discussions on the forum for driving single RGB LEDs which is probably the best way to start, including -
https://picaxeforum.co.uk/threads/picaxe-rgb-controller.9747
Using a single 4-leg RGB LED, common cathode or common anode, and even with just one resistor in the common line, one can start experimenting with them, three resistors, one per LED, is a better way.
A PICAXE with three separate PWM channels is perhaps best and easiest to use, but a single PWM and multiplexing the LEDs with three digital lines, or just pulsing digital lines to 'bit-bang the PWM' can also work.
Unfortunately this forum, like most others, doesn't support searching for short words like "RGB LED" and similar but Google and other internet search engines can help there, especially when the "site:" is specified, for example -
rgb led site:www.picaxeforum.co.uk