How to design a passive filter from poles and zero of a transfer function?
For a second-order network it is rather simple:

Compare the coefficients of both transfer functions: (1) The generalized function with the factors a and b, resp. and (2) the function applicable to the chosen circuit configuration (involving L an C).

Of course, both functions must have the same form (polynominal in numerator and denomonator). From this comparison, you get (at least) two equations for calculating the parts values.