What's the difference between a monohybrid and dihybrid cross?

A monohybrid cross considers only a single character whereas a dihybrid cross considers two characters (and a trihybrid cross would consider three characters, and so on).  

For example, if you cross pure-breeding tall pea plants with pure-breeding short pea plants, you are considering only 1 character: stem length.  That is a monohybrid cross.  If you cross pure-breeding tall, round-seed pea plants with pure-breeding short, wrinkled-seed pea plants, then you are considering 2 characters in the cross and it is a dihybrid cross.



When crossing 2 heterozygotes in a monohybrid cross involving a character that follows complete dominance, the Mendelian genotypic and phenotypic ratios are:
1:2:1 (1 homozygous dominant: 2 heterozygous: 1 homozygous recessive)
and
3:1 (3 individuals show the dominant phenotype for every 1 that shows the recessive phenotype)

When crossing 2 heterozygotes in a dihybrid cross involving a character that follows complete dominance, the Mendelian phenotypic ratios are:
9:3:3:1 (9 show dominant phenotype for both characters: 3 show the dominant phenotype for one character and the recessive phenotype for the other character: 3 show the recessive phenotype for one character and the dominant phenotype for the other character: and 1 shows the recessive phenotype for both characters.


How you do a cross depends on the organism.  For pea plants like Mendel used, sometime you allow them to fertilize one another and other times you cover their flowers so that they can only self-polinate: or, you may manually pollinate by dusting the pistil with pollen.