In-place upgrades
A usual server upgrade might need to consider moving services and data from the current virtual machine to the new one. On the other hand, in-place upgrades let's you start with a small server and upgrade as you go without much hassle. Even better, if you aren't upgrading disk space the change is fully reversible.
So, how to actually upgrade? Go to the server you want to change and click on the big button saying Upsize Droplet. Then you are free to choose the option you want to:

And that's it. Allow for a small downtime and you are ready to go.