* You're already moving: You, me, and everything on Earth are constantly moving through space. We're orbiting the Sun at a speed of about 67,000 miles per hour. We're also moving with the Earth as it rotates on its axis. So, in a way, we're always traveling in space.
* Unaided speed is relative: "Unaided" is a bit ambiguous. If you're talking about the speed you can reach by jumping, running, or any other means without external propulsion, it's pretty slow compared to the vastness of space. You wouldn't be able to move significantly faster than the speed of your initial motion from Earth.
* Spacecraft speeds: To travel at significant speeds in space, we need spacecraft. They use rocket engines to accelerate to much higher speeds. These speeds can vary, but they are typically much higher than the speed of Earth's orbit.
So, the answer to your question depends on how you define "speed" and "unaided."
If you're thinking about the speed you could reach by jumping on a space station, it would be very, very slow. If you're asking about the speed at which you're currently moving through space because of Earth's motion, it's around 67,000 miles per hour.