Ok, I'm trying to wire this transformer

I've got from MPJA, however I'm not really sure if my thinking is correct. One side (left) will be connected to 120V AC and from the other I'm looking for an output of 12V AC. How should I connect the wires ?

 

For 120vac power input, on the primary AC side (left in your pic), wire the two black wires together and then the two red wires together and then wire your 120vac source to the resulting red and black wires.

The reason they provide two 120 volt winding is that you have the option to connecting them in series and supplying 240vac as some countries use for home power wiring.

On the output side you will have 12vac on the two blue wires and that is all you will need to feed a full wave rectifier. The center tapped wire, yellow, is useful for other rectifier schemes or for bi-polar DC supplies.

Make sense?

 

On the left side, tie the two reds together and the two blacks together.
You should use a fuse on the "hot" wire to protect the circuit in case you have a short somewhere. If you don't have a fuse holder, Radio Shack carries them. I suggest a panel mount type:
http://www.radioshack.com/product/index.jsp?productId=2062230
A 1 or 2 amp fuse should be sufficient.

Use a 3-wire pre-made cord to wire it up. The black wire is "hot", the white wire is "neutral", and the green is earth ground. Connect the transformer's two red wires to the neutral wire, and the two black wires to the side tab on the fuseholder, and your "hot" lead to the bottom terminal of the fuseholder. Adding a power switch is a good idea. The fuse should always be the first thing in the circuit, though.

Make certain that the wires are well-insulated. I like to use a couple of layers of heat-shrink tubing. Don't use "electrical tape", the adhesive used will get gummy over time and the tape will fall off.

Connect the ground wire to the chassis of your project.

On the right side, you'll get 12VAC between the two blue wires.

 

Thank you very much leftyretro and SgtWookie for your speedy help. I really appreciate it and I'm glad that there are people like you who can provide a professional advice. Hats of the heads for you.