Step 1: Concept
Nickel in $[Ni(CN)_{4}]^{2-}$ is in the +2 oxidation state ($3d^8$ configuration).
Step 2: Meaning
$CN^{-}$ is a strong field ligand, causing pairing of electrons in the $3d$ subshell.
Step 3: Analysis
Pairing leaves one $3d$ orbital vacant. Hybridization occurs using one $3d$, one $4s$, and two $4p$ orbitals.
Step 4: Conclusion
The resulting hybridization is $dsp^2$, leading to a square planar geometry.
Final Answer: (C)