Connecting a Red/Green LED Cluster to an Arduino
A typical Arduino solution would be something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

See other Q's here about calculating resistor values and choosing transistors.

For example a suitable value for R2 might be (V2 - Vf(d2))/If(d2) where If &lt;&lt; If(max).

See also Switching 9V using a NPN transistor and an Arduino



Here's that circuit





With only 1V of headroom between V2 and Vf, uncertainty in Q2's Vce(sat) may make it hard to pick R2 without some conservative experimentation. 

You might therefore also find it fun to look at Olin's answer to this other question and Alexan_e's answer to this one and work out a solution that would work better. You can't use Olin's answer directly because you have a common-anode LED-module that needs a low-side switch. But PNP solutions can often work in a complementary way to NPN solutions, so long as you take into the account the subtleties referred to in Alexan_e's comment (and described more fully in his answer linked to above). (n.b. there may be other gotchas)