How can I determine molecular geometry?

VESPR stands for valence shell electron pair repulsion. This theory basically says that bonding and non-bonding electron pairs of the central atom in a molecule will repel (push away from) each other in three dimensional space and this gives the molecules their shape.

We can use the following notations when examining a Lewis structure of a molecule.
A = central atom
X = peripheral atoms
E = non-bonding electron pairs of the central atom

$A {X}_{2}$ = linear molecule (example $C {O}_{2}$)
$A {X}_{3}$ = trigonal planar (example $A l {H}_{3}$)
$A {X}_{3} E$ = trigonal pyrimidal (ex. $N {H}_{3}$)
$A {X}_{2} {E}_{2}$ = bent (ex. ${H}_{2} O$)
$A {X}_{4}$ = tetrahedral molecule (ex $C {H}_{4}$)