You can view the Running on DigitalOcean guide to learn how to set up a server.
Separate database and web server
In this setup you have a database running on its own machine that allows remote connections. Your web server is running on a different machine with Umami installed and connects to the database remotely to store and retrieve data.
In this setup, you would have an app hosting provider host the Umami app for you. You would still need a database running elsewhere that the app could connect to. Here are a few app hosting providers that can host Umami. Vercel and Netlify both have a free tier available.
A managed database is where the host provides you with a running database that you don't have to install or maintain. Here are some providers for managed databases.