We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field regimes. We show the importance of symmetry, and demonstrate how it can be used to simplify the variational wave functions. We present in detail the algorithm for efficient wave function optimization. We also present a Monte Carlo-based diagonalization technique to solve the quantum dot problem in the strong magnetic field limit where the system is of a multiconfiguration nature. PACS numbers: 71.10.-w, 73.21.La, 02.70.Ss 1.