Quantum CNot algorithm problem
The other answers explain how the circuit behaves. This answer will explain how to directly manipulate the circuit into a simpler form.

Here's a surprising fact: surrounding a CNOT with Hadamards flips the CNOT.



(I get that checking this on paper requires already understanding the solution to your question. You can confirm it for yourself in a circuit simulator such as Quirk at least.)

Your CNOT circuit is surrounded by 3 Hadamards. By flipping the CNOT, and using the fact that H is its own inverse, we can turn that into a single Hadamard:



Leaving us with the standard make-an-entangled-bell-pair circuit. So, when the input is $|00\rangle$, the output is $\frac{1}{\sqrt 2}|00\rangle + \frac{1}{\sqrt 2}|11\rangle$.