You wont be controlling a dozen LEDs with an 8 pin Picaxe as it only has 4 output pins, but programming the 08M Picaxe is exactly the same as the rest of the Picaxe family, you just have to take case which options you try and use as not all chips are teh same

Make sure you get some 10K and 22K resistors for building the programming interface, if you have an old serial mouse then you can cut the cable from that and use it as a programming cable.