What conditions would have to occur for an offspring to express the recessive trait?

Both parents would have to have one recessive gene.

Explanation:

Blond haired people have two recessive genes to have blond hair. Dark hair is dominant over blond hair. If B represents dark hair and b represents blond a person could have the two genes B and b. The dominant gene will win. For example: Bb produces dark hair. BB produces dark hair, but bb produces blond hair. Two blond haired people each will give a b characteristic to the offspring, producing blond hair. Two parents with Bb genes each have 1/2 chance of giving a b gene. Therefore two dark haired parents Bb have 1/4 chance of having a blond offspring. 1/2 times 1/2 gives 1/4 chance (if they have both the dominant and recessive genes). Two parents with BB can not have a blond haired offspring.