Only the workspace owner can change or cancel the plan. It's all under Settings → Billing → Subscription (open your profile menu and choose Administration), on the page titled Plan & billing.
Find Pro or Business on the Subscription page and click Get started. The Change your plan dialog opens:

The new plan is active as soon as the payment is confirmed, and your billing period starts that day. To compare what each plan includes, see the pricing page.
For now, our team makes the switch for you. Raise a ticket with the plan, billing period and number of seats you want, and we'll switch it.
Don't buy the new plan from the plan page while your current one is active. That starts a second subscription alongside the first.
You can cancel at any time. On the Subscription page, click Manage subscription. Stripe's billing portal opens, and you cancel your plan there.

The plan cancels at the end of the current billing period, and nothing changes until then. The Subscription page shows the date your plan is set to cancel and confirms you keep full access until then. On that date the workspace moves to Free.
By cancelling. There is no Free option on the plan page: when your paid plan ends, the workspace moves to Free automatically.
Nothing is deleted, and nobody loses access. What changes is how much you can add.
Stripe tries the card again over the following days. Update it straight away with Manage subscription, so the next attempt goes through.
If the renewal is still unpaid a couple of days after the renewal date, the workspace moves to Free. Your plan comes back once the payment goes through. While the workspace is on Free, Manage subscription isn't shown, so to update the card at that point, raise a ticket. If the payment can't be collected at all, the subscription ends and the workspace stays on Free. Either way, nothing is deleted. Invoices and payment problems lists the usual causes of a failed payment.
Cancelling stops the next renewal; the current period is not refunded automatically. For a refund request, raise a ticket.
Related: Plans & billing explained · Seats: adding and removing people · Payment methods and AI credit top-ups · Invoices and payment problems · Contact support