How do I get actual values from a Jacobian matrix?

ClearAll[f]
f[x0_, y0_] := D[{Sqrt[x^2 + y^2], ArcTan[x, y]}, {{x, y}}] /. {x -> x0, y -> y0}

f[0.3, 0.5] // MatrixForm

I would caution you against using MatrixForm in the definition, as that would leave you with results that cannot be easily used in further computation.