In exchange for the interest rate you receive, the bank expects to keep your CD for the full term. If you decide you want to redeem your CD before it matures, expect to pay a penalty. Ask the institution how it calculates redemption penalties. You may wish to consider redeeming a CD only if deposit rates elsewhere have risen more than enough to make paying the penalty cheaper than missing out on higher rates. Stock brokerages also sell CDs.
Brokers also promote their CD rates as being among the highest.
If you buy a CD through a broker, the FDIC advises you to ask the broker where your CD will be deposited. Know when your CD is scheduled to mature. The financial institution will contact you as your CD reaches maturity to ask what you want to do with the proceeds. Most institutions have automatic rollover programs that give you a period of 10 days or so to tell it what to do. If you don't reply, the institution will likely renew the CD for the same term, only at the current deposit rate.