You may think that you are standing still. You are on the surface of a planet rotating at a thousand miles per hour. (Here in Columbus, Indiana at a latitude of 39.2 degrees, we are only moving at 803.6 MPH.) The Earth orbits the sun at 67,000 miles per hour or 18.6 miles per second. (This changes slightly because the Earth's orbit is not exactly circular, but elliptical. Since the Earth is the closest to the sun on January 3rd, the perihelion, that is when it would have the most velocity. Since it is the farthest from the sun on July 4th, the aphelion, that is when it would be moving the slowest.)
Our entire solar system orbits the center of the Milky Way Galaxy at 514,000 miles per hour or 143 miles per second. This is roughly 1/1300 the speed of light. Still, it takes 230 million years to travel all the way around the galaxy.
The universe is expanding. Most of the galaxies are moving away from each other. The Milky Way Galaxy, which you are a part of, is moving at 1.3 million miles per hour or 361 miles per second. This is roughly 1/515 the speed of light.