In Settings > Billing, view your current plan. In this example, we're on the Bronze Plan.
Click the 'Change Plan' button at the top of the page. This will display your upgrade/downgrade options. Then choose the plan you would like to move to and click either Upgrade or Downgrade. A confirmation box will appear.
What Happens When Upgrading
If you're upgrading, then you'll be charged a prorated amount instantly and your service will be upgraded. So getting more storage, bandwidth, and features can be done at the drop of a hat.
When Happens When Downgrading
On the flip side, if you're downgrading then your service will remain on the current plan until the end of this billing period. You'll then be moved to the lower plan and charged the lower amount.