Quantum decoherence is one of the most substantial challenges on the way to fullyfledged quantum technology. Noise mitigation based on dynamical control techniques, aside from error correction, is known to be another effective approach to protect qubits from decoherence. In this thesis, we studied the dynamics of a spin qubit interacting with a disordered spin bath in different dimensions. By modeling the environmental spins from fundamental dipolar couplings and employing Monte-Carlo simulations, this research provides an insight into the precise driving and control of a noisy spin qubit, including the noise distribution, decoherence mechanism, driving error, gate fidelity, and performance of dynamical decoupling sequence. This knowledge will be helpful to the future design of noise-robust quantum gates and potential decoupling protocols of spin qubits.