Look at the flat dash-wedge diagram. Then draw the chair and visualize the pair (or more) of subsitutents.
1,2 axial = 1,2 equatorial = trans
1,3 axial = 1,3 equatorial = cis
1,4 axial = 1,4 equatorial = trans
1,5 axial = 1,5 equatorial = cis
1,6 axial = 1,6 equatorial = trans
conversely, if one of the substituents is "flipped" to the other position, so does the conformation.
1 axial, 2 equatorial = 1 equatorial, 2 axial = cis
1 axial, 3 equatorial = trans
1 axial, 4 equatorial = cis
1 axial, 5 equatorial = trans
1 axial, 6 equatorial = cis
It's pretty convenient once you look at the big picture. My starting point is: 1,2 axial is obviously trans because the point opposite directions. Each additional carbon away flips the cis/trans conformation, each axial-equatorial difference flips the cis/trans conformation.
So a 1,3 cis cyclohexane has to be both axial or both equatorial, whereas a 1,4 cis cyclohexane has to have one axial and one equatorial substituent, but a 1,4 trans cyclohexane again has both axial or both equatorial substituents.