Making the coils is probably the most time consuming part of building an accelerator. It's also the most formulaic: follow the process and it'll turn out just fine.
Step one: Figure out what material to make the accelerator barrel out of. It should not be ferromagnetic, otherwise it'll direct the magnetic fields away from the projectile (ex: don't use steel). It should be non-conductive, otherwise there will be eddy currents from the coils firing and you'll waste energy (ex: don't use aluminum, brass, or carbon fiber). You'll need to put sensors on it. Reflective sensors are a pain, I recommend cut-beam sensors. If you don't want to drill a bunch of little holes and then spend a lot of time aligning them, try to find a material that's infrared see-through. I've found that semi-rigid nylon tube fits these bills. You can buy it from smallparts.com. If you do, I also recommend getting a steel rod to put through it and keep it straight till you mount it.
Step two: Setup a place to actually wind the coils. Get two blocks, drill two holes in them and use this to hold the coil up. If you mount the block of wire somehow, you can then just turn the barrel to make the windings.
Step three: Winding them. You'll probably have to make several levels of coils. If you do this all at once, they'll slide all over, look like shit, and generally not be of the right shape. Instead, do one level at at time and use gorilla-glue to hold each layer in place before putting on the next layer.
Step four: Adding the shielding around them. The best shielding possible is ferrite torroids used for transformers. In general, if you can design your coils to fit within such torrioids you'll get the best focusing. As for the sides, I just use iron filled epoxy (such as quick steel) but I'm not sure if that's the best material.
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