Both very non-conductive and conductive armour can work. If you wear a full-body suit of armour and get hit by lightning, the current will travel through the armour rather than through you.
This assumes that the suit is continuous and there is no place where one piece of armour does not touch the adjacent piece at all (It's OK if it has holes, if the armour is made explicitly for protection against lightning the pieces would probably be connected by wires to make sure they never completely detach).
If subject to repeated strikes conductive armour could start heating up and eventually melting. To protect against this the most conductive metals would have to be chosen. The more conductive the metal the less heat is created when current flows through it. Gold may still not be a good choice due to its other properties though.
As Cort Ammon mentioned, very high energies, such as those found in natural lightning, may still remain dangerous, so it would be a good idea to coat such a suit of armor with unconductive material on the inside to increase the resistance of the path lightning would have to take to go through you.
If the armour is a worse conductor than the air the lightning will travel through the air rather than through you.
This kind of armour is a bit more problematic. For this to work the armour has to completely cover the wearer, otherwise the lightning will just pass through the hole and then through you.
For this to work the armour would have to be very unconductive, as you being a pretty good conductor can counteract the resistance the armour offers otherwise.
The air through which the lightning passed would also heat up a lot and that could burn you if it is close enough (Assuming the lightning was artificially made to strike exactly where you are, this would be on the very first layer of air on the outside of your armour, which is very close).
Metal also will never be less conductive than (pure) air, so this armor would need to be made of a non-metal.
Partial armour works only in the first case. If you wear a helmet and breastplate but no leg pieces and get hit by lightning, the lightning would travel through the armour where possible and through your legs where there is none.
In the second case partial armour is just like armour with a particularly big hole.
As for the material; any metal works. All metals are more conductive than you + clothes + air between you and the armour.
As commenters and other answers have mentioned, conductive armor would effectively act as a Faraday cage. The link offers a good explanation of how these work.
Edit: Shalvenay did the math, a real lightning bolt is simply too strong even for very conductive armour (which is to say that even if its resistance is very low, the energy dissipated as heat is still sufficient to cook the wearer). Unless your conjured lightning bolts are less energetic (like those produced by tesla coils. They can be stronger than those, but not as strong as lightning), short of a superconductor no armour could really protect you. This is especially true if you're subject to multiple strikes.
When electricity flows through any medium, part of its energy is converted into heat. This property is commonly used in electric stoves, but should usually be minimized. This isn't much of a problem in everyday circuitry since most metals have such a low resistance that the produced heat dissipates quickly enough to not cause any notable increase in temperature, however, the energies involved in a lightning strike are so vast that even the small fraction of them which are converted into heat by their traversal of the metal are large enough to damage the "circuit" (i.e. melt the armor) and its inhabitant. The same effect is the reason why we can see lightning - air has a much higher resistance than metal (which is why lightning rods "attract" the bolt). The energy dissipated when lightning passes through air is strong enough to heat it to the point that it turns into plasma. Similarly, when current passes through the human body it will heat it up, potentially destroying parts of it if the current is strong enough (e.g. if it is a lightning).