Are tesla coils safe?

Echo is correct, these can be very dangerous, specially to the inexperienced. I have many years in engineering, and I'd never get close to one.

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Tesla Coil Safety

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RE:

Are tesla coils safe?

to make? And how can I convince someone that they are/arent?

A Tesla coil and the parts associated with it can definitely be dangerous. The hazards are:

Lethal voltages and currents in the primary circuit. (Electric shock). This is always so, even for small ones. The voltages are higher than spark plug voltages so can get out of control and appear in very unexpected places.

Sufficient energy at high freqencies in the secondary circuit to cause serious RF burns deep inside tissues. This is unlikely to be more than 1 kW in a homebuilt one, but that can be bad.

Because of the extreme voltages and currents associated with high voltage and resonance, components can explode or disintegrate, and perhaps generate toxic fumes.

Some old high voltage components you could acquire have tranformer oils in them which contain PolyChlorinatedBiphenols (PCBs) - toxic in unpleasant ways.

Large amounts of plazma generated in the air, implying ozone gas with toxicology in small amounts like carbon monoxide or cyanide gas. The PEL (Permissable Exposure Limit) for ozone is 0.1 ppm. Compare with 10ppm for HCN (cyanide gas).

Annoying the hell out of neigthbours who may then come over and shoot you {:-) This is from loud noise, flashes and serious interference to radio and television. It could frighten them into drastic action.

Components left seriously charged after it is turned off.

The hazards are reduced but not eliminated entirely by smaller ones. In some areas you are not allowed to build them at all because of these issues, and the likelihood of inexperienced builders. There is no part of these things that you can consider as safe, or even closely approachable, because breakdowns and faults are so common because of the extremes (vaguely defined extremes at that) to which they are driven. Incidentally you need a larger room to run one in. There is the likelihood of damaging any electronic equipment nearby. Can you imagine one of those streamers in the eye?

Energy hazards are usually managed by defining where and when the energy can and cannot be, and controlling the energy accordingly. A big Tesla coil can lead to almost uncontrolled energy wandering around in a volume, and it operates in a system with few or poor specifications. Yes you can switch it off.

As far as convincing someone they are safe, I guess by lying. It is a calculated risk, like riding a bike downhill backwards. Operators really need to know what they are doing. It is no device for practical jokes and fooling around. Incidentally if you look at some of those pictures of people with giant streamers leaping onto them they are usually fuzzy so you can't see the metal grid over them like a cage.

The high voltage is stored by capacitors on the circuit board. If the TV or monitor hasn't been plugged in for a few days, all should have discharged, but to be on the safe side, short circuit each of the capacitors in turn with an insulated handled screwdriver.

It depends but I'd stay safe and not try it if the person is actually trying to make one, but doesn't know how, is not prepared and is not using the right equipment of course.

Wisegeek is the best source for science questions: http://www.wisegeek.com/what-is-a-tesla-coil.htm

It depends. The risk is mostly associated with the electrical energy you will be dealing with and how big it will be. If you do not use very much energy, there is very little risk (unless you drop it on your foot). Find some plans which include detailed instructions covering proper operating procedures and design operating conditions.

Yes if you follow the directions for insulating the parts that you are not supposed to touch.

Many science museums have them and run demos in which audience members touch their output. Try taking that someone to see that museum show.