Hi there! I'm not sure if this is really what you're looking for, but I used 5mm LEDs (I used 5mm because I needed them to provide a soft light inside a gingerbread house; 3mm would work just as well on the outside of a cake) on my Christmas cake this year and it was my first time using them. As someone who knows nothing about electrics, here are my tips!
- I picked up all the things I needed (LEDs, battery case, extra wire, resistor) from Maplins (an electronics store in the UK); I'm certain pretty much any specialist electronics/hardware store would stock all these things, and you can also order them online.
- Do your research! I spent a lot of time figuring out how many LEDs I wanted, and therefore what power sourse and resistor I needed. If you wire them wrongly you could blow the LEDs or have them not light up bright enough.
- I made my circuit food-safe by running the wires through a tube within the cake, but if something like that isn't possible for your design I'd recommend wrapping them in something. And it's a good idea to insulate all your connections with electrical tape too.
Hope that was helpful!