Gauge theory is a powerful theoretical framework for understanding the fundamental forces in the standard model. Simulating the real time dynamics of gauge theory, especially in the strong coupling regime, is a challenging classical problem. Quantum computers offer a solution to this problem by taking advantage of the intrinsic quantum nature of the systems. The Schwinger model, that is the 1+1 dimensional U(1) gauge theory coupled to fermions, has served as a testbed for different methods of quantum simulation. Using a trapped-ion system with up to six qubits, we simulate the real-time dynamics of pair creation in the lattice Schwinger model, the Schwinger model with discretized space dimension, for times much longer than previously accessible. In this talk, I will discuss the integrated theoretical, algorithmic, and experimental approach we used to achieve this result. Specifically, I will compare the gate requirement for two formulations of the model using the Suzuki-Trotter product formula, and explain the trade-off between errors from the ordering of the Hamiltonian terms, the Trotter step size, and experimental imperfections. I will also present the result regarding the effectiveness of a recently proposed symmetry-protection protocol by Tran et. al. and a symmetry-inspired post-selection scheme for mitigating experimental errors.