The circumference of the Earth at the equator is 25,000 miles. The Earth rotates in about 24 hours. Therefore, if you were to hang above the surface of the Earth at the equator without moving, you would see 25,000 miles pass by in 24 hours, at a speed of 25000/24 (1666 Km Per Hour) or just over 1000 miles per hour.

Multiply by cosine of your latitude to see how fast the Earth is rotating where you are.

Earth is also moving around the Sun at about 67,000 (67,000*1.6  Km ) miles per hour.

Advanced Answer

If by "turning" you mean the rotation of the Earth about its axis (where axis just means the straight line between the North and South poles) it is quite easy to figure out how fast any part of the Earth's surface is moving.

The Earth rotates once in a few minutes under a day (23 hours 56 minutes 04. 09053 seconds). This is called the sidereal period (which means the period relative to stars). The sidereal period is not exactly equal to a day because by the time the Earth has rotated once, it has also moved a little in its orbit around the Sun, so it has to keep rotating for about another 4 minutes before the Sun seems to be back in the same place in the sky that it was in exactly a day before.

An object on the Earth's equator will travel once around the Earth's circumference (40,075.036 kilometers) each sidereal day. So if you divide that distance by the time taken, you will get the speed. An object at one of the poles has hardly any speed due to the Earth's rotation. (A spot on a rod one centimeter in circumference for example, stuck vertically in the ice exactly at a pole would have a speed of one centimeter per day!). The speed due to rotation at any other point on the Earth can be calculated by multiplying the speed at the equator by the cosine of the latitude of the point. (If you are not familiar with cosines, I wouldn't worry about that now, but if you can find a pocket calculator which has a cosine button you might like to try taking the cosine of your own latitude and multiplying that by the rotation speed at the equator to get your own current speed due to rotation!).

The Earth is doing a lot more than rotating, although that is certainly the motion we notice most, because day follows night as a result. We also orbit the Sun once a year. The circumference of the Earth's orbit is about 940 million kilometers, so if you divide that by the hours in a year you will get our orbital speed in kilometers per hour. We are also moving with the Sun around the center of our galaxy and moving with our galaxy as it drifts through intergalactic space!

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