Where you manage the subscription depends on where you bought it.
Bought on the website
Open Settings on desktop, go to the Account tab and choose Manage Subscription. It opens the billing portal in your browser, where you can change the plan or update the card. Manage Subscription on the phone points a web subscription back to the web, though Cancel Subscription works on both, see Canceling below.
On the Sync plan the same tab has an Upgrade to Grape Pro button. Your subscription moves to Pro at once, the difference for the rest of the month is charged right away, and the next renewal is at the Pro price.
Bought on the phone
Subscriptions purchased on iOS or Android are managed through the App Store or Google Play subscription settings, like any other app subscription. Moving from Sync to Pro is a purchase of the Pro plan on the Account screen, which the store treats as an upgrade of the subscription you have.
Restore purchases
New phone, reinstalled app, or the paywall showing even though you paid: tap Restore purchases on the Account screen and your purchase is looked up and reapplied.
Canceling
Open Settings, go to Account and choose Cancel Subscription, under Sign out. Grape asks why you are canceling first: pick the answer that fits best and, if you like, add anything else you want us to know. Something else asks you to say what it was before the button works. Every answer is read by the people who make Grape.
A subscription bought on the website is canceled right there, on desktop or on the phone. It keeps working until the end of the period you already paid for, and the Account page shows the day it ends in place of the button. Changed your mind before then? Manage Subscription on desktop turns renewal back on.
A subscription bought on the phone can only be canceled in the App Store or Google Play, so after your answer the button reads Continue and opens your subscriptions there, where you finish the cancellation. On desktop it opens the store's subscriptions page in your browser.
Canceling stops renewal, and your notes are never held hostage: everything local stays local, in a database file on your device. Export and backups are part of the paid plans, so take an export before the subscription ends if you want your notes as files.
Folders and notes you share pause when the plan ends: the people in them can still read, nobody can edit, and sharing picks up again when you subscribe.
If something is stuck
Write to support with the platform you subscribed on and the email you used, and a person sorts it out.