Basic genetics terms
Genes come in different versions called alleles. A dominant allele (written with a capital letter, e.g. T) is expressed whenever present; a recessive allele (lowercase, e.g. t) is only expressed when no dominant allele is present -- so an organism needs two recessive alleles (tt) to show the recessive trait, but only one dominant allele (TT or Tt) to show the dominant trait.
Monohybrid inheritance
Crossing two heterozygous parents (Tt x Tt, each carrying one dominant and one recessive allele) produces offspring in a predictable ratio.
Example 1: Cross two pea plants that are both heterozygous for height (Tt x Tt, where T = tall is dominant, t = short is recessive). Find the expected genotype and phenotype ratios of the offspring.
The possible offspring genotypes are TT, Tt, Tt, and tt (1:2:1). Since both TT and Tt show the tall phenotype (T is dominant), the phenotype ratio is 3 tall : 1 short.
Natural selection and evolution
Natural selection is the process by which organisms with characteristics better suited to their environment are more likely to survive and reproduce, passing those characteristics to their offspring. Over many generations, this can shift a population's characteristics -- the basis of evolution. Variation within a population (from mutations and sexual reproduction) provides the raw material natural selection acts on.
Example 2: In a population of moths, a dark-coloured variant becomes more common after tree trunks in the area become covered in soot from pollution. Explain this using natural selection.
Against sooty, darkened tree bark, dark moths are better camouflaged from predators than light moths, so more dark moths survive to reproduce. Over generations, the proportion of dark-coloured moths in the population increases -- natural selection favouring the trait best suited to the changed environment.