Since 99% of the visible universe is made up of plasma, you won't have to go far to find plasma, which as you correctly guessed, is the fourth state of matter. You can find it by looking up at the sun, at a fluorescent light bulb that's turned on, or in a bolt of lighting. The explanation of plasma is not too complicated. When you melt ice into liquid water, the water molecules (composed of two Hydrogen and one Oxygen atoms) go from being confined in the crystalline solid state to being able to freely flow like they can in the liquid state. If you heat that liquid water up so that it boiled, you would form water vapor that makes up the gas phase where the water molecules can freely bounce around and have large spacing between them. I've just described the three states that you know of: solid, liquid, and gaseous. The fourth state, plasma, happens when you continue to heat up that water vapor so hot that the actual Hydrogen and Oxygen atoms that make up the water molecules are able to move independently from each other with large spacing between them just as individual vapor molecules were able to travel in the gaseous state.

Yes, plasma is the fourth state of matter, but keep in mind that there are more than one state of solid matter as well: a glass is very different from a crystal, for example, and a single substance can have multiple crystal states as well (e.g. graphite and diamond are both carbon, but they are very, very different states of matter with remarkably different properties).

Plasma has properties quite unlike those of solids, liquids or gases and is considered to be a distinct state of matter.

We say plasmas are the fourth state of matter after solid, liquid, and gas. If you start with a solid and heat it, it melts and forms a liquid. If you heat it even more, the liquid evaporates into a gas. If you heat it even more, the gas molecules break apart into separate atoms, but we still call it a gas--just chemically changed. Eventually at very high temperatures, usually thousands of degrees, the electrons get ripped off the atoms, and then it's a plasma.