Detonation depends on what compound you are using. You need to pick a poison. Black powder, smokeless powder, or something more exotic.
With low explosives like the two mentioned above, very easy to come by and very dependent on how they are packed. The tougher the case, the bigger the boom, generally. If the case it too tough it won't do anything until punctured, melted, etc. You just end up with a pressurized case. To weak of a case and you get a fire, or at best a vent or jet of hot gas.
Bullets and explosions, don't count on it. You can take a live round and whack away on it with a hammer with no ill effects. When I have to pull a bullet from a round, the puller is actually a hammer shaped case that holds the case. Then you pound it onto something and the bullet eventually comes free. I never worry about setting one off (though I do tend to keep my face away from the primer, just in case). Even IF you manage to set one off, it'll basically be like a firecracker and throw some brass shrapnel from the case at the worst. I think most just split, dislodge the bullet, and vent. As said, you need a chamber to make a cartridge work, and a barrel if you want any kind of velocity from the bullet.
Black powder can be bought just about anywhere, google it. Smokeless powder can be ordered from gun or sporting good magazines (Natches, Cabellas, etc) and it's fairly cheap. I think my last 1lb bottle was about 20 bucks, maybe 30. Buy it in 8 pounders, save some cash. Also it can be purchased in brick-n-morter gunstores without paying the $25 hazmat fee.
Triggers, movies and books love cellphones. You just need to add heat to the above propellants, some (crystalized high explosives) require a concussion wave from a blasting cap. I don't like the cell phone idea because they tend to be low power devices by themselves, however. Take the speaker leads and run them to an SCR transistor, a relay, or some other switch, and you can run higher current through the switch to set off the explosive. Cheap "fuses" on these electrical circuits would be something like the ignitors for model rockets. Two thin pieces of wire, wrapped with a small amount of fabric. Burns hot with a fairly low voltage, around 6V or 4 AA batteries in series. Conversely you can hook up a couple capacitors from radioshack to some 9V batteries to charge and you have all the current you will need. All it takes is a switch to dump the energy on the igniter.
Remote starters can be taken from any remote device, toys, deer feeders, etc. Wired devices are easier but you need a long wire and they are traceable (obviously). Cell phones work better when they just control the switch, as 3.7V from that little NiCd is going to need one hell of an igniter to actually light something. It could, but you run a possibility of failure. Same for any timed device. Device controls switch, switch connects igniter to power source. If the device is strong enough, it can also act as the power source.
