It's the second time I advertise for this blog, so I guess I'll just say that I'm not affiliated with the blogger in any way! The best resource I could read on VQE was Musty Thoughts' article on it. In fact, it's the first part of an ongoing series on variational algorithms, where he explains not only how they work, but also their limitations and the challenges they have to overcome in the future. Definitely worth checking it out.
Some frameworks wrote tutorials on thse kind of algorithms. For instance, Qiskit has a tutorial on how to apply VQE to chemistry problems and a short tutorial on how to use the
Estimator primitive to solve a variational problem.
Xanadu on the other hand also wrote a tutorial to run VQE with Pennylane and made a YouTube video on it.
In fact, VQE's such an important algorithm that I think that most frameworks would have their own tutorial on how to implement it. For instance, you could also find a tutorial for cirq here. It's thus up to you to choose the framework you're the most proficient with!
From what I've seen, most of these tutorials only assume basic knowledge of Quantum Computing (not in chemistry), so you should be fine with at least one of them.