How does Lysander fall in love with Hermia?

Egeus, Hermia's father, speaks to Theseus in act 1, scene 1, asking him to forbid Lysander to marry Hermia. According to Egeus, Hermia has fallen in love with this young man because Lysander bewitched her. Egeus outlines all the ways Lysander has wooed his daughter. Hermia says she considers Lysander, not her father, a god.
As for Lysander, we get much less of an explanation, though the many ways he has sought Hermia testify to a man besotted and lovesick. Lysander states of Hermia:

My love is more than his [Egeus's].

Lysander also implies he loves Hermia because she is "beauteous," or beautiful.
Helena offers more insights, saying that Lysander loves Hermia for her eyes, her voice, and her fairness. But she also notes that love is like an irrational child. It doesn't need a logical reason to love. Once a person decides to love someone, he or she turns all the beloved's features into beauties. Helena states:

Things base and vile, holding no quantity,
Love can transpose to form and dignity.
Love looks not with the eyes but with the mind.
And therefore is winged Cupid painted blind.
Nor hath Love’s mind of any judgment taste—
Wings and no eyes figure unheedy haste.

Lysander's largely unexplained love for Hermia thus perfectly fits the play's theme of love as a form of lunacy or madness, a way of being that is without rational basis.

Lysander and Hermia are in love before the play begins, so we do not get to see their courtship. But we can infer from what they say about each other that they are typical young people in love, drawn to each other by physical attraction and an idealized version of what the beloved one is.
They are suited to each other by class and status, which is what Lysander emphasizes in the beginning of the play when Hermia's father openly prefers Demetrius to him as Hermia's suitor, so, again, we can assume they had many opportunities to see and appreciate each other on social and court occasions.
Through the magical twists and turns of A Midsummer Night's Dream, we can believe that they are restored to what is perhaps a more mature love by the end of the play . . . unlike Helena and Demetrius, who are together only because the love potion was never removed from Demetrius's eyes.