Orbits are possible due to centrifugal force. The faster something is going (in angular velocity, which you can think of as "the speed at which it goes around something" or "the times it goes around a thing in a minute/day/year/whatever"), the stronger the centrifugal force and the closer to earth you can orbit.
Mass doesn't matter, or rather it cancels itself out. There's a mass term in the formula for centrifugal force: F = m * [d^2 r]/[d t^2] which means Force = mass times the angular velocity (the change in direction around something divided by time, just like normal velocity is the change of position divided by time), squared (meaning multiplied by itself). Angular velocity is often written as a lower-case Greek letter omega: ω. Thus, we can re-write the formula for centrifugal force as F = m * ω * ω. There's also a mass term (actually, two of them, one for each object, but for this purpose we treat the earth as fixed and are only concerned about the satellite's mass) in the formula for gravity: F = G * m1 * m2 / r^2 which means that the Force of gravity is equal to the Gravitational constant (you need to know this to determine the actual force as a number, but for now, just ignore it) times the mass of the first object (earth) times the mass of the second object (the satellite), all divided by the radius (the distance between the objects' centers) squared (multiplied by itself).
In order to orbit at a specific height (commonly called an "altitude"), your outward (centrifugal) force must equal your inward (gravitational) force. Thus, to orbit at height r (from the center of the earth) you solve this formula: m * ω^2 = G * m1 * m2 / r^2. Since the mass of the satellite is on both sides of the equation, you can simply divide both sides of the equation by that mass - it doesn't matter what it is! - and you have a simpler equation that gives the same result: ω^2 = G * m1 / r^2. If you plug in all the numbers into that, it will tell you how fast anything needs to be going around the earth in order to orbit the Earth at a given height.
Since gravity falls off rapidly as you go further out - something twice as far as you from the center of the earth experiences only one fourth as much gravity - stuff that is relatively close to earth (things in low earth orbit, such as the International Space Station) have to go around the earth really fast; the ISS (and everything else at the same height) does it in about 90 minutes. That's only a few hundred miles (or a few hundred kilometers) above the earth's surface. Many times that far away - about 26.2 thousand miles, or 46.2 thousand kilometers - stuff orbits in exactly one day, which means they always pass over the same spot on the equator every day. If they orbit over the equator directly, they don't appear (from those of us on earth) to move at all. This is useful for communication and TV satellites; you can point a fixed satellite dish at them. Much further out still, at 385 thousand kilometers, you have the orbit of the moon, which takes about 27.3 days (just shy of four weeks). These are just three examples of different orbital heights around earth.
You can demonstrate this easily yourself if you have a yo-yo or similar (really, any string with a weight on the end). Start with a long section of string, at least two feet long (60 cm) and spin it around your hand just fast enough to keep the string tight and have the weight make a full circle. Now shorten the string a bunch, to maybe eight inches (20 cm) and again, spin it fast enough to make a full circle. You should notice that, with the shorter string, you have to spin the object a lot faster to keep the string tight, but you can keep it tight at the different distances. The tension in the string stands in for gravity, here; if the string is loose, gravity would overcome your centrifugal force and crash your satellite. If you spin (orbit) so fast that the string is under too much tension and breaks, that's like going so fast you leave earth's orbit (though unlike a string, gravity never "breaks"; it's more like it would just stretch out, letting the satellite fly away and exerting a weaker and weaker pull to try and bring it back).
Hope that helps!