Stereocenters are atoms where changing configuration leads to generation of a different stereoisomer. These might be sp2 carbons (defining cis/trans or E/Z isomerism of double bonds), or sp3 carbons (defined as "centers of chirality").

A stereogenic carbon atom that is a "center of chirality" satisfies two criteria:
-It must be sp3 hybridized
-It must have 4 different things attached to it.

Look at the following molecules and locate the stereogenic atoms.  Not all molecules will have stereogenic atoms.

Molecule
Mirror Image
Notes

R-Bromochlorofluoromethane

S-Bromochlorofluoromethane
Probably the simplest possible example:  4 different atoms connected to carbon.

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Spacefilling model
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Ball & Stick
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E-2-butene

Z-2-butene
Alkenes provide examples of stereochemistry that are important. It's not so much the atoms as the bond that provides the origin of steroisomers (though of course to change the configuration, we need to break and re-form bonds to one of the two atoms in the double bond).

R-1-amino-1-phenylethane

S-1-amino-1-phenylethane
Another fairly simple example:  carbon has NH2, a phenyl ring, methyl, and H.
This illustrates how we may have to step out several bonds to find a point of difference between any of the groups attached to the stereocenter.

Cyclohexanol

Cyclohexanol
No stereogenic atoms!  The two CH2 groups are identical.
See if you can identify an internal mirror plane of symmetry.
This compound is achiral.

S, S-trans-Cyclohexanediol

R, R-trans-Cyclohexanediol
Each oxygen-bearing carbon has 4 different substituents:  H, OH, CH2, and CH(OH).

This compound is chiral.

cis-Cyclohexanediol

Each oxygen-bearing carbon has 4 different substituents:  H, OH, CH2, and CH(OH).

However, because of internal symmetry, this molecule is achiral.  The mirror image is superimposable, although we must ring-flip one of them first.

D-alanine

L-alanine
A simple amino acid; the central carbon has CO2-, NH3+, methyl, and H attached.

Morphine

Unnatural Morphine
A complex molecule; clearly chiral.  Several stereogenic atoms.