Learn Italian: Saprò il mio destino dall'oroscopo. - I will know my destiny from the horoscope.

Saprò is the future tense of sapere (to know). Sapere is an irregular verb in the future tense: it drops the e from its stem. So, instead of following the regular pattern to become "saperò", it shrinks down to saprò.

Why use sapere instead of conoscere for "to know" my destiny?

In Italian, sapere is used for knowing facts or pieces of information, while conoscere means to be familiar with a person, place, or complex topic. Since your destiny is treated as a piece of information you can find out, sapere is the correct choice here.

Why is there an "il" in "il mio destino"? Doesn't "mio" already mean "my"?

Yes, but in Italian, possessive words like mio almost always need a definite article (like il or la) right in front of them. The main exception is when talking about singular family members (like mio padre), but for regular nouns like destino, you must include the article.

How does "da" become "dall'" in this sentence?