The way I understand it is that when you put shunt the current starts flowing more into the shunt resistance than the galvanometer, Then how can galvanometer give a correct value for actual current of circuit? And why does putting a resistor make the current flow through it? Doesn't current flow in path of least resistance?
You need to understand the purpose of galvanometer and of ammeter.
Ammeter is connected in series with the circuit ,so full current under measurement pass through it. It is used to calculate large currents. Galvanometer is used to measure small currents and needs very small current for zero to full scale deflection (usually in mA).
If you have a 5A current in a circuit. You put a galvanometer in series and total 5A current will try to flow through it, the galvanometer coil will be burnt. Therefore, you have to limit the current which can be achieved by putting a big resistance in series or a very small resistance in parallel.
Now if you add a big resistance in series, it will also drop the voltage, and effect the overall circuit, so we don't use it.
Second option is putting a parallel resistance (shunt) with very small value so that most of the current flows through it and only a tiny portion of current will flow through galvanometer (as current always have a tendency to flow in less resistant path like you mentioned) which is sufficient to make the deflection.
How do we know the correct reading? We know the resistance of shunt and we just plug in the numbers.
I should have clarified more on the purpose of galvanometer. You are right about the fact that the current reading from the galvanometer would not be accurate and also it can't be used for higher value of currents. We have ammeter for that. Key is in knowing when to use which instrument: Galvanometer has a lower accuracy but a much higher sensitivity than ammeter. Also, galvanometer tells you the direction of current as well.
If you want to measure a current then use ammeter. If you want to know if there is a current and which way its flowing then use galvanometer. It just happens that it can get fairly decent reading on how much current is going through your circuit. Its a lab instrument that you can use to find voltage as well as current based on how you set it up and get "close-enough" values that are good for simple experiments.