Vector representation of wavefunction in quantum mechanics?

I am new to quantum mechanics, and I just studied some parts of "wave mechanics" version of quantum mechanics. But I heard that wavefunction can be represented as vector in Hilbert space. In my eye, this seems almost improbable. How does this work? Can anyone present an example and how it gets converted to vector form?

So I am referring to Dirac Bra-ket formulation of quantum mechanics.