A simple (but very inefficient) transformer can be made by wrapping some wire around a nail, then wrapping another coil around the first coil; alternatively, the second coil could be wrapped around the nail adjacent (next to) the first coil. The difference in voltage between the coils will be equivalent to the ratio of turns in each coil (ie, if both coils are the same number of turns, you have a 1:1 ratio - if one coil has 10 times as many turns as the other, you have a 10:1 ratio, etc) - minus losses due to inefficiency (and the fact that this isn't an ideal world).
Once again - the above would be merely "good enough" for a simple demonstration (ie - kid's science-fair project) - not for actual work. Real transformers use special materials in thier construction to minimize losses, eddy currents, etc to gain efficiency. They also don't tend to use solid cores (indeed, you could dispense with the nail entirely, and build an "air-core" transformer) - instead they use cores built up of laminated steel plates.