Diastereoisomers and enantiomers

Stereoisomers have identical composition and atom-to-atom bonding sequence, but they differ in the arrangement of the atoms in space. 

Enantiomers are stereoisomers that are nonsuperimposable mirror images of one another.
 
Enantiomers have the opposite configuration at all stereogenic centres.

Example:  Trans-1,2-dichlorocyclohexane has two stereogenic centres.  These are not mirror images of one another.  Therefore this compound exists as two enantiomers.


More about R and S in cyclic compounds
Choose an assymetric carbon that has the H pointing back.
Give the groups attached to that carbon priorities.
Cl (1) CHCl (2) CH2 (3)
If, from highest to lowest, the order is clockwise, the configuration is R.
 
  Diastereoisomers are stereoisomers that are NOT mirror images of one another.
Diastereoisomers have some (but not all) stereogenic centres with the opposite configuration.
 
Example: cis-1,2-dichlorocyclohexane and either enantiomer of trans-1,2-dichlorocyclohexane are diastereomers.

The configuration at C-1 in cis-1,2-dichlorocyclohexane would be R (same as at C-1 in trans-1,2-dichlorocyclohexane).

The configuration at C-2 in cis-1,2-dichlorocyclohexane would be S (opposite to the configuration at C-2 in trans-1,2-dichlorocyclohexane).