Subtleties of Boost Conver (Step-up Converter)
How many Henry the inductance should be?


Here are some pointers but, bear in mind this is a big topic and I can’t cover all the subtleties.


Start by defining the maximum power and the regulated voltage on the load. This should be easy. Let’s say it’s 10 watts and 10 volts just as an example.
Think about the switching frequency to be used. A pretty common frequency is 100 kHz but anything up to and beyond a couple of MHz might be contemplated. I assume 100 kHz for this answer.
The maximum power divided by the switching frequency equals the energy to be liberated from the inductor during each switching cycle on full load. Controlling the PWM duty cycle ensures that the output voltage remains constant on lighter loads. For this example, energy per cycle (W or work) is 100 uJ maximum.
Now think about the input voltage and how low it might drop before the converter stops operating. It might be nominally designed to be powered from 5 volts and you might choose 4 volts as the bottom limit.
So, at 4 volts on the input you want to store at least 100 uJ of energy in the inductor. Because we want to have a sensible duty cycle range, we know that the duty cycle will be close to the maximum in this scenario but, let’s not be greedy; choose 90%.
Armed with knowledge of the input voltage and the on-time (determined by duty and frequency) and, how much energy we wish to store, we can calculate the inductance value.
The important formulas that determine this are


$$V=L\dfrac{di}{dt}$$

$$W=\dfrac{L i^2}{2}$$

I have to say at this point that I’m assuming the converter is what is known as operating in DCM. DCM stands for discontinuous current mode and it is underpinned by all the energy that was stored in the inductor being fully used in each switching cycle. It’s probably more intuitive to help beginners understand what happens and how the interactions play out in DCM.

The other mode (CCM) I’ll leave for the OP to investigate.


  What is the formula of the output voltage according to these
  parameters.


Better to understand what happens and derive it yourself. I never really have a formula; I always do the mental thinking about stuff first because it reminds you what are the important things to consider.