How do I know what letters to use if I want to make a Punnett Square?

Let's say for example the problem states that the mother has brown eyes and the father has blue eyes. Blue eyes is a recessive gene (and your problem should specify which is which) There is homozygous and heterozygous. Here is a list:

recessive = bb (b for blue eyes)
Dominant = BB (homozygous)
Hetero = Bb

recessive = brbr (br = brown)
Dominant = BRBR
heterozygous = BRbr

BB- homozygote dominant (purple flowers)
Bb-heterozygote (purple/white flower...has the gene of BB and bb)
bb- homozygote recessive (white flowers)

  B   B
b Bb Bb
b Bb Bb

The offspring will all be heterozygote (Bb), and will show the dominant phenotype...which would be purple in this case, but in the next generation, then 1/4 will be bb (white).

ok so the letters have to do with dominant or recessive traits.
a dominant trait is like the stronger trait. brown eyes is the dominant trait over blue eyes. When it is a dominant trait, the letters for the punnet squares will have to be BB or Bb. most of the time the teacher will say dominant heterogeneous (Bb) or dominant homogeneous (BB).

a recessive trait is the "weaker" or lighter trait; in our eye example, blue eyes would be the recessive trait. For the recessive trait to show, it has to be recessive homogeneous; or bb.

in conclusion; if the teacher says something like you are crossing a heterozygous dominant with a homogeneous recessive.... you would cross Bb with bb