how do you find the lowest energy of a chair conformation?

Answer 1

The answer above explains the chair conformation, which I'm guessing you already know. Consider a cyclohexane molecule with a methyl group coming off of it. There are two chair conformations possible: one with the methyl group in an axial position and one with it in an equitorial position. In the axial position, the methyl group has significant steric interactions with the axial hydrogens pointed the same way. In the equitorial position, the methyl group is pretty much out of the way of everything. To find the lowest energy conformer, draw out the two chair structures and find which has the least steric interaction. Ring strain should be fairly constant. For approximate energies, check your textbook. Certain things should be fairly apparent, like that the interation of an axial methyl group and a hydrogen would be less than that of two axial methyl groups.

Answer 2

The chair conformation is a term used for the most stable chemical conformation of a six membered single bonded carbon ring. In the lowest-energy chair conformation, half of the 12 hydrogens are in axial positions, which means their C-H bonds are parallel and appear to stick up and down from the structure, the other half are in equatorial positions; meaning that they are splayed out.