The basic circuit just needs a few extra components.
Adding C2 gives it a DC gain of 1 but keeps the AC gain set by Rf,Rg (G= 1+ Rf/Rg)
Adding R1,R2 creates the mid point DC offset at the non inverting input.
Adding R3 and C4 creates a smoothed supply (low pass filter) for this offset.
Adding C1 decouples the input.
Adding C3 decouples the output
R3 and C4 ensure that the voltage to the potential divider (R1,R2) is as noise free as possible. Any noise on the potential divider would appear at the (non-inverting) input and be amplified.
With regard to values:
R3 was chosen to be less than 1% of R1,R2 so that it would not drop too much voltage before the potential divider. C4 value was chosen because it is a commonly used value and gives a low break frequency .
These values are not particularly critical and others could be substituted if needed