They're closer to analog computers than digital, but really they're neither and share some similarities of both. In the sense that the qubits usually only have 2 measurable states in computation, they're similar to digital computers, but that only goes for when you measure. On the other side, the 'programs' going in are not really digital information (though they can be represented as such), and because qubits are not only in one of 2 states (unlike bits) the way in which you interact/program them is definitely not digital, it is analog.
If you're interested in learning about writing quantum programs, I recommend checking out IBM's Qiskit toolkit[0]. I found the tutorials to be helpful for helping grasp the fundamentals of quantum programming.
Are there any resources you particularly recommend if I wanted to learn more about quantum computing and how quantum computers work on the hardware level?