S-plane poles,zeros to components without table
The classical procedure is as follows:

1.) Given is the transfer function H1(s) to be realized (for example, derived from required pole-zero locations or from other knowledge sources).

2.) You select one of several realization methods (filter circuits) and the corresponding transfer function H2(s) of the circuit (expressed through parts values).

3.) If both functions H1 and H2 are of the same form (nominal form) you can compare the corresponding polynomial expressions (factors of s and s²). From these equations you can derive formuas for finding the parts values. In nearly all cases you start with a definition of an impedance niveau (choosing a basic R or C value).     

EDIT: Example to step 3:

For a simple RLC-lowpass (2nd order) the transfer function is 

H2(s)=1/[1+sRC+s²LC] 

From the general system theory we know that any second-order lowpass transfer function (expressed through the pole locations) is:

H1(s)=Ao/[1+s/(Qp*wp)+s²/wp²] with Qp=pole Q and wp=pole frequency.

Comparing both functions it is an easy task to see that LC=1/wp² and SQRT(L/C)=R*Qp. Hence, you have two equations for three unknowns (select L or C). The pole data (Qp, wp) are given parameters (they characterize the lowpass form: Butterworth, Chebyshev,...).