You will see your first interest earned in your account at 4 p.m. ET two business days after you start using Gemini Earn, and more compound interest arrives every day at 4pm after that. For example, if you move funds to Earn on Monday, you will earn interest on this starting Tuesday, but the balance in your account will not reflect until Wednesday at 4 p.m. ET. If you move your funds to Earn on Saturday, which is not a business day, you will earn interest starting Monday, but the balance in your account will not reflect until Tuesday at 4 p.m. ET.
Your confirmation e-mail will tell you when you can expect the first payment to appear.
Do I get the price appreciation of crypto too, or just the interest payments?
Your crypto participating in Earn stays as crypto the entire time. So if the price of the crypto changes in fiat (USD) terms, your Earn balance will also change in USD terms. Your interest payments will be in crypto, so you are always earning more crypto while participating in Earn regardless of the USD value. See also Why can Earn balances appear to decrease?