Learn French: Je lui fais confiance, alors je lui pardonne.

In English, you "trust him" and "forgive him" directly. But in French, both of these actions require the preposition à (to): faire confiance à and pardonner à. Because they use à to connect to a person, you must use the indirect object pronoun lui (to him/her) instead of the direct object pronoun le.

If this sentence means "I trust him", how would I say "I trust her"?

It would be exactly the same: Je lui fais confiance, alors je lui pardonne. The French indirect object pronoun lui means both "to him" and "to her". You have to rely on context to know the person's gender.

Why is the verb fais (do/make) used here to mean "trust"?

In French, "trust" is often expressed with a phrase rather than a single verb. The expression is faire confiance à (literally "to make trust to"). Because je is the subject here, the verb faire is conjugated as fais.

Why does lui go before the verb instead of after?

In French, object pronouns are placed immediately before the verb they are connected to. While in English we say "I forgive him" (putting the pronoun after the verb), the French structure is je lui pardonne (literally, "I to him forgive").