On the billing page you'll see an option to 'Update Plan' as shown below:
There you'll see the other plans available and you can click on 'Downgrade' to change to a plan with fewer features or 'Upgrade' to move to a plan with more features.
When you downgrade then you'll get billed for the new plan at the end of your current billing period.
When you upgrade you'll move to the better plan instantly. You'll get billed for the difference in price between your current plan and the new plan pro-rated on how many days are remaining in your billing period.
For example: You're currently paying $47 per month for your plan. Halfway through the 30 day billing period you upgrade to the $97 per month plan.
You'll get a credit for the unused time on the $47 per month plan ($23.50). This will be applied against the payment for half of the $97 plan ($48.50). In total, you'll get billed $25.