How to calculate Type 1 error and Type 2 error probabilities?

Null Hypothesis: ${\displaystyle H_0:\mu ={\mu }_0}$
Alternative Hypothesis: ${\displaystyle H_1:\mu <,>,\ne {\mu }_0}$
Type 1 errors in hypothesis testing is when you reject the null hypothesis ${\displaystyle H_0}$ but in reality it is true
Type 2 errors in hypothesis testing is when you Accept the null hypothesis ${\displaystyle H_0}$ but in reality it is false
We can think about:
Probability of event ${\displaystyle \alpha }$ happening, given that ${\displaystyle \beta }$ has occured:
${\displaystyle P\left(\alpha \mid \beta \right)=\frac{P(\alpha \cap \beta )}{P\left(\beta \right)}}$
In light of this, the Type 1 and Type 2 errors in hypothesis testing are as follows:
Type ${\displaystyle 1}$ = ${\displaystyle P}$( Rejecting ${\displaystyle H_0}$ | ${\displaystyle H_0}$ True)
Type ${\displaystyle 2}$ = ${\displaystyle P}$( Accept ${\displaystyle H_0}$ | ${\displaystyle H_0}$ False )