Have a look at Digikey's LED range sometime, sorted by colour. There's actually quite a lot of variation in forward voltage for a given colour, even within the "indicator" category.
It's very straightforward.
So:
+12V to anode of segment.
Cathode of segment to drain of N-channel MOSFET.
Source of MOSFET to 0V rail (common ground of +5V and +12V rails).
Gate of MOSFET driven from microcontroller I/O pin.
Pulldown resistor from gate to source of MOSFET (to prevent floating MOSFET gate during reset etc) - 10k or 100k is fine.
It's also common to insert a low-value resistor between the microcontroller output and the MOSFET gate - something like 47 ohms - because of the MOSFET's gate-source capacitance, but this is probably not important with a small MOSFET that's not being switched constantly.
When firmware drives the pin high, the MOSFET conducts and illuminates the segment.
Traditional MOSFETs BS170 and 2N7000 will work. 2N7000 is slightly better; it has a guaranteed RDSon of about five ohms at Vgs=4.5V.
A much better option is the Zetex / Diodes Inc ZVN4206:
http://www.digikey.com/product-detail/en/ZVN4206AV/ZVN4206AV-ND/190158
This has a guaranteed RDSon of 1.5 ohms at Vgs=5V and 500 mA drain current.
An even gruntier alternative is Vishay Siliconix IRLD110:
http://www.digikey.com/product-detail/en/IRLD110PBF/IRLD110PBF-ND/812489 which is packaged in a 4-pin 0.3" DIP (optocoupler style).
There are other MOSFETs that have better specifications, including several (NTD4906N, NTD4963N and NTD4815N) from ON Semiconductor, but they have much higher gate capacitance and are a bit out-of-place, even though they are cheap.
All the devices I've suggested here are through-hole (wire leaded). Most are TO-92 or E-line.