The trapped ions platform represents an excellent framework for Quantum information science experiments. Long coherence times, extremely high state initialization and detection fidelity, inherent full-connectivity between qubits are some features that make trapped ions the ideal qubits. It is the same features that make this platform extremely suitable for quantum simulation of various physical phenomenon, particularly quantum spin models. In this thesis, I present the design and construction of an ion trapping apparatus for quantum simulation experiments. This apparatus is operational and is used for the trapping of ionized Yb atoms. The 6 electrodes of the trap, two of which are needle electrodes, are made out of tungsten. I discuss the unique technique we use to make tungsten needle electrodes. The design, construction, and testing of the Yb source, used to produce a thermal beam of Yb atoms, is also discussed.