How do I change plan or update my payment method?

Go to your account settings, Billing / Subscription section. There you'll see your current plan and can switch plans (the change takes effect immediately or at the next period, depending on the direction).

For the payment method, update your card in the same place: the next charge will use the new one. Your invoices are also available for download there. To compare plans in detail, the Pricing page sums up what's included in each.