I'm having trouble understanding when to use the first or second verb conjugation. Could someone throw up some examples?
There is no difference in use. They are just verbs with their meanings. Each belongs to either the first or the second conjugation, just like nouns belong to the first, second or third declension (or have gender, or animacy) - an intrinsic trait of each verb.
Conjugation governs the postfixes (endings) of the personal forms of verbs. All first conjugation verbs have "-ет" or "-ёт" ending in 3rd person singular present tense. All second conjugation verbs have "-ит" ending in 3rd person singular present tense.
There are exceptions, but your favourite book should tell you about those.
Examples can be found on this page.