Transition metal dichalcogenides based on transition metals (like Mo, W, Ta) and chalcogens (like S, Se, Te) are important two-dimensional (2D) materials in materials research for a range of applications including but not limited to electronics, photonics, optoelectronics, sensing, and photovoltaics. At the scale of the dimensions of these materials, the properties differ from their properties at larger dimensions. To exploit these interesting properties for novel applications, the growth methods of the materials are an important aspect. While materials research has advanced over several decades in this area, substantial challenges exist in their controlled and rapid growth. MoTe2 is an especially challenging material to grow among the TMD materials and needs more investigation given its superior properties. In this thesis, I report the study of the parameters of growth mechanisms of materials like MoTe2, MoSe2, and MoS2 on SiO2, Si, and GaN substrates. I present reproducible growth of MoTe2 in an ultra-high vacuum (UHV) environment using co-deposition of transition metal and chalcogen. The phase diagram developed for this system shows that both semimetallic and semiconducting phases of MoTe2 can be grown on SiO2 substrates. With the addition of a MoS2 underlayer, the phase of MoTe2 is affected significantly. A similar growth mechanism can be used to grow MoSe2. The quality of the materials is investigated using Raman spectroscopy, photoluminescence spectroscopy, cross-sectional transmission electron microscopy, scanning electron microscopy, low energy electron diffraction, X-ray photospectroscopy, energy dispersive spectroscopy, and electrical characteristics.