Open the service under Services > My Services and use the Upgrade/Downgrade option on that page. You will be shown the price difference before anything is confirmed.
How the money works
A change part-way through a billing period is prorated. The system calculates the unused value of your current plan and applies it against the new one, so you are charged the difference over the remaining days rather than a full period at the new price.
On a downgrade, the unused value usually becomes account credit rather than a refund to your card. That credit is then applied automatically to your next invoice, which is why a later renewal can appear cheaper than expected or not charge your card at all.
This is different from changing your billing cycle, which takes effect at the next renewal rather than immediately. See the article on billing cycles if that is what you actually want.
Before you upgrade
Make sure the upgrade solves the problem you have. If you are running out of space because of an uncleaned cache directory or a log file that was never rotated, a bigger plan will fill too — later, and more expensively. The article on disk usage, bandwidth and inodes explains how to tell which limit you are actually hitting, and they are not interchangeable.
Before you downgrade
Check that your current usage fits inside the smaller plan first. Downgrading into a plan you already exceed causes problems immediately. Look at disk usage, mailbox count and any feature the smaller plan does not include.
Take a backup you hold yourself before any downgrade. Do not rely on the platform to preserve something the new plan does not support.
Changes that are not self-service
Moving between plans on different platforms, or any change that involves a migration rather than a resize, is not a button. Open a ticket, tell us what you want to end up with, and we will tell you what is involved. That conversation is free; an unplanned migration is not.