Upgrade: client area → Services → My Services → the service → Upgrade/Downgrade. The difference is pro-rated to your next invoice and the change is immediate; nothing needs migrating because you stay on the same infrastructure. The price you upgrade to is then held for three years, like everything else.
Downgrade: same place. Check the smaller plan's limits first (websites, mailboxes, storage) — if you're over them the downgrade will need a tidy-up first, and we'll tell you what.
Cancel: Services → My Services → the service → Request Cancellation. Choose end-of-billing-period (the default) so you keep what you've paid for. There's no contract on hosting or email plans. Website design retainers need 30 days' notice, as set out when you signed up.
Before you cancel hosting, three things to think about: your email — mailboxes go with the account, so copy anything you need first (or ask us to help move them); your domain — it stays registered to you and can be transferred out at any time, but if it renews through us you'll want a new provider lined up; and your website files — download a backup from cPanel → Backup Wizard.
Leaving because something isn't working? Tell us first. Most of the reasons people give are things we can fix the same day.