How do I predict the shape and bond angle of an molecule?

Electron pairs arrange themselves so they are as far apart as possible (electron pair repulsion theory). In a covalent compound, the number of electron pairs around the central atom determines the shape of the molecule. 

An electron pair shared between two atoms is called a bonding pair (BP)

An electron pair on one atom only- not shared- is called a lone pair (LP)

BeCl₂ has two bonding electron pairs shared between the Be²⁺ ion and the two Cl^- ions. Cl-Be-Cl  bond angle = 180 degrees (linear)

BF₃  has three bonding electron pairs shared between the B³⁺ ion and the three F^- ions. The  bond angle = 120 degrees (trigonal)

CH₄ has four bonding electron pairs shared between the C^4- ion and the four H⁺ ions. The  bond angle = 109.5 degrees (tetrahedral)

However when we introduce lone pairs to the molecules it distorts the bond angle because of electron pair repulsion.

Electron pair repulsion theory tell us that LP-LP repulsion > LP-BP repulsion > BP-BP repulsion.

Therefore a molecule containind three bonding pairs and one lone pair like NH₃ (four electron pairs all together) gives rise to a distorted bond angle because the lone pair repels the other bonding pairs which decreases the bond angle from 109.5 (tetrahedral) to 107 (pyrimidal).