The terms "Enantiomers" and "Diastereomers" are tongue-twisters, but they rely on a couple of very simple definitions:
  • Two stereoisomers that are mirror images are enantiomers.  The prefix enantio- designates the mirror-image relationship.
  • Two stereoisomers of the same compound that are not enantiomers are diastereomers.  This is a fairly broad definition, as we'll see.
When comparing two molecules to find their relationship, the "decision tree" goes as such:
  • Are they, in fact, stereoisomers?  The connectivity must be identical, otherwise they are constitutional isomers and not stereoisomers.  An example would be butane vs. 2-methylpropane.
  • Are they identical?  (Check to make sure!  This can trip you up if you aren't careful.)  If they are truly stereoisomers and not identical, then they must be either enantiomers or diastereomers.  You may need to reorient one of them to see--or you may need to rotate about single bonds, or do cyclohexane ring flips in order to see if they are simply different conformers of the same molecule.
  • Are they mirror images of each other?  If yes, they are enantiomers.  The caution about reorienting and looking at other conformations is important.
  • If you get to this point--they are stereoisomers and they are not enantiomers, then they are diastereomers.
Look at some examples.

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Spacefilling model		 Wireframe
Ball & Stick
Show R/S

Examples of enantiomers

All stereocenters have inverted configurations

L-alanine
D-alanine

(R, R)-cyclohexane-1,2-diol
(S, S)-cyclohexane-1,2-diol

Diastereomers: stereoisomers that are not enantiomers

At least one stereocenter is the same, at least one is different. And anything in between.

(R, R)-cyclohexane-1,2-diol
(R, S)-cyclohexane-1,2-diol
There are some useful (and important) considerations regarding absolute configuration (R vs. S at stereocenters) and these relationships:
  • If two molecules are enantiomers, the absolute configuration of every stereocenter is inverted going from one enantiomer to the other. 
  • Therefore, if any one stereocenter is identical (and at least one differs), then the molecules are diastereomers.
  • Stereoisomers need not have stereocenters:  E and Z alkenes are the common example of diastereomers.   There are also classes of molecules that are chiral but have no stereocenters (we'll be ignoring these). 
  • Likewise, molecules may have stereocenters but be achiral. If there is an internal mirror plance of symmetry, that destroys the chirality because every sterecenter reflects into its mirror image elsewhere in the molecule.

But wait...

E/Z isomers of alkenes are "stereoisomers that are not enantiomers" too! So they are diastereomers. The double bond is the non-chiral source of the stereochemistry.

E-2-butene
Z-2-butene