Design mostly comes down to which resistors to use.
Let's make a few assumptions: Power source is about 5 volts and the LEDs inside the package are about 3 volts for Green and Blue and 2 volts for Red. The package is "Common Anode", but see below for "Common Cathode"
If you just wanted a full 20mA Blue LED, you could leave out the resistors for Red (R-R) and Green (R-G) and then the blue voltage drop would be 2 volts for about 20 mA. Resistor = Volts/Amps = 2/0.02 = 100 Ohms.
For Cyan, we're leaving out the Red light component, so we could put another 100 ohm resistor for Green (R-G), but is that really Cyan or more of an Aqua. Also, if you increase both resistors, you won't necessarily get a dimmer version of the exact same shade.
Ultimately, design for the exact color you want will require some experimentation and rather that soldering and desoldering multiple resistors, I recommend a breadboard to tune first and then record and apply your combination of resistors and apply power.
As to the "Common Cathode" solution, really the only difference is that the common pin is the complimentary voltage, so just switch the polarity when you apply power and everything else should be equivalent.
The RGB Adapter is available in multiples of 4 from 4 to 16 pieces
Schematic is above
Simply stated, there are three resistors, one for each color inside the 4 pin led. Depending on your voltage source, and desired mixed color you'll need to calculate what values you need.
The circuit is designed for a Common Anode 4 Pin LED. For "Common Cathode" all you have to do is reverse the power connection (Ground goes to '+' and Positive goes to '-'). The orientation of the LED package should be the same.
Traces are limited to about 500mA, but the LED itself will likely be limited to around 60mA total.
Layout is above
Board is 19mm x 19mm x 1.6mm
The footprints are for standard 1/4 watt resistors and Common Anode 4-Pin RGB LED. Common Cathode can also be used ... see design section.
Power connection is NOT standard 2.54mm pitch. Positive and negative are both 4.5mm from top edge and each is 7.5mm from it's respective side's edge and 4mm from each other.