It really depends on where you’re moving from :-).
DigitalOcean is not a shared hosting provider (like HostGator, GoDaddy etc - just as a few examples), so when you deploy a Droplet, your deploying a blank Operating System that you would need to be able to configure, secure, optimize etc.
When you deploy a Droplet, you’d need to install & configure the web server (NGINX, Apache, Caddy etc) as well as any of the programming languages needed (PHP, Ruby, RoR, Python, NodeJS etc), the database server (MySQL, MariaDB, Percona etc) and so forth. It’s not already setup for you.
DigitalOcean does offer pre-configured images for WordPress and various other pieces of software, though ultimately, you need to know how to manage and work with the CLI and OS to really be able to effectively manage your setup (and ensure that it’s secure).
How you’d move depends on your current needs. If you’re using WordPress, for example, you can either use their image or go through the process of setting up as described above. You would then backup your data, database etc and use either SFTP or SSH to transfer the files over (SSH would require that your current web hosting provider provides SSH access, otherwise you’d be limited to SFTP).