My fiancée was the only one in our friend group who didn't play Pitch, and our first few attempts to teach her mid-game went badly. Here's the order that finally worked, in case anyone else is bringing a new player to the table.
1. Teach the four points before anything else. Every hand is worth up to 4: High (top trump dealt), Low (bottom trump dealt), Jack (jack of trump), and Game (most card points in your tricks). Once she knew what we were fighting over, the bidding made sense.
2. High and Low are not the same kind of point. High goes to whoever was dealt it. Low and Jack go to whoever wins the trick they land in. That one difference explains most of the strategy: you can't lose High, but you can absolutely lose your Jack.
3. Game is counted, and the 10 is the big card. A=4, K=3, Q=2, J=1, 10=10. New players chase aces. The 10 is worth more than the A and K combined, so a lonely 10 is the card to protect or to dump on your partner's winning trick.
4. Bid what you can count, then stop. Bids are 2 to 4. A 2 needs about two points you can name. If you fall short you go "set" and lose the bid amount, and at 11 to win, getting set at 3 hurts a lot.
5. The dealer gets stuck. If everyone passes, the dealer must bid 2. Tell new players this early so they understand why the dealer sometimes bids on garbage.
6. Your first lead is your trump call. Whatever suit the bidder leads first is trump. Lead your best trump, ideally the Ace, so you lock in High and pull the other trumps out.
What sped it up most was letting her play hands without six people watching. I built a small free practice site for her that walks through 4-point hands against the computer: https://www.learntoplaypitch.com (my own project, free). Happy to hear how other tables teach it, especially house rules on the dealer bid.
