It's very rare that monsters drop items (weapons, armor, shield, etc.). For example, I've been playing this game nearly every day for 3.5 years, and I've seen about 10 or 15 item drops.

The main way to get new items is to craft them using recipes. See the wiki page Crafting. Also, work your way through the rank missions. They explain a lot about crafting, and they give you various recipes (some good, some bad).