Step 1: Recall the relationship between hybridization and molecular shape.
The hybridization of the central atom in a molecule determines its electron geometry and, subsequently, its molecular shape (considering lone pairs).
Step 2: Match each hybridization with its corresponding shape.
\begin{itemize}
\item A. dsp$^2$: This hybridization involves one d, one s, and two p orbitals, resulting in a square planar geometry. Matches with I. Square planar.
\item B. sp$^3$: This hybridization involves one s and three p orbitals, resulting in a tetrahedral geometry. Matches with II. Tetrahedral.
\item C. d$^2$sp$^3$: This hybridization involves two d, one s, and three p orbitals, resulting in an octahedral geometry. Matches with III. Octahedral.
\item D. sp$^3$d: This hybridization involves one s, three p, and one d orbital, resulting in a trigonal bipyramidal geometry. Matches with IV. Trigonal bipyramidal.
\end{itemize}
Step 3: Combine the matches to find the correct option.
The correct matching is A - I, B - II, C - III, D - IV.
Final Answer: The final answer is $\boxed{A - I, B - II, C - III, D - IV}$