The personal "a" is your clue
When conocer is followed by a person, Spanish requires the personal a: Conozco a tu madre. If you find yourself writing saber a [person], that's a red flag — switch to conocer.
Saber + infinitive = can
One of the most useful patterns in Spanish: saber + infinitive expresses ability. ¿Sabes nadar? means "Can you swim?" (do you know how to). This is different from poder, which expresses being physically able or having permission — see our poder vs saber guide for the full comparison.
Preterite changes meaning
Both verbs shift meaning in the preterite: supe means "I found out" (not just "I knew"), and conocí means "I met" (not just "I knew"). Supe la verdad ayer = I found out the truth yesterday. La conocí en Madrid = I met her in Madrid.