how are satellites put in orbit?

Really tall people throw them.

Ok..it was just a guess.

They are sent there on top of rockets.
Satellites can be categorised as Low Orbit or High Orbit.
For the lower ortbit ones. a speed of 17,500 mph is sufficient.
The high Orbit Satellites are used for Geocentric Orbits of 500 miles or more from the surface.
The power needed is added usually by an extra rocket Stage.

The satellite(s) is in the tip of the rocket under a fairing that separates during launch and then the satellite is released into orbit, with the rocket falling back to earth. Ther are a variety of orbits, usually defined by their altitude. The altitude determines the speed the satellite must travel at

Satellites are put into orbit using chemical fuel rockets. The rockets are typically multi-stage, with the first stage being the largest, the second stage the next largest, and so on. As each stage finishes burning through its fuel, the empty fuel container is ejected and falls to Earth and the next stage ignites. The satellite is in the payload capsule at the tip of the rocket.

The mass of the fuel needed to lift the satellite into orbit is much greater than the mass of the satellite itself. This is because Earth's surface gravity is fairly strong and thus to orbit the Earth or leave Earth's gravity you have to go very fast to avoid falling back down. AND because there are no gas stations in space so all of the fuel you need you have to bring with you. These factors are quantified in the famous Tsiolkovsky rocket equation,

vf - v0 = ve ln(m0/mf)

where vf is the final velocity, v0 is the initial velocity, ve is the exhaust velocity, ln( ) is the natural logarithm function, m0 is the mass of the fuel and the payload, and mf is the mass of the payload only.

The velocity you need to orbit the Earth is v = √(GM/r), where G is the universal gravitational constant, M is the mass of the Earth, and r is the average distance between the orbiting satellite and the center of the Earth. For low Earth orbits, which are common, the satellite is quite close to Earth so r is basically the same as Earth's radius, and in this case v = 7.8 km/s.

If you want to escape Earth's gravity entirely (and go to Mars, for example), the rocket must reach or surpass Earth's escape velocity. The escape velocity for a planet of mass M and radius R is v = √(2GM/R). For Earth that's v = 11 km/s.

If you're putting a satellite into orbit, the orbital velocity must be the final velocity from the rocket equation, vf = √(GM/r)

To save on fuel costs, or send up a bigger satellite for the same amount of money, you can take advantage of the Earth's rotation. The closer to the equator you launch your rocket, the larger v0 from the rocket equation will be, which minimizes vf - v0. This is why the major US launch areas are in Texas and Florida: southern states. This also means that most satellites have prograde orbits (they orbit the Earth in the same direction that the Earth rotates), which also means that although a rocket launch begins vertically (they rise straight up into the sky for a long time), as they get higher and higher they start to angle and fly toward the east.

about 3500

A (artificial) satellite is (or several are) put in the top (or tip) ofa huge rocket & launched into Space. At a certain height the satellite separates & gets into its own orbit around the Earth.

With a giant slingshot

Rockets; it's the only way to give them enough speed, and get high enough above the atmosphere, to obtain orbit.

The satellite rides a rocket since the space shuttle is no longer flying. It is accelerated vertically then the rocket is tilted to the East to take advantage of the rotation of the earth.
Depending on the function of the satellite it can be placed in low earth orbit at 17,000 mph or raised with a booster rocket to a higher orbit, such as a geosynchronous orbit.
Sometimes satellites are placed in different orbits such as a polar orbit

With rockets.

With rockets. They need to be above the Earth's atmosphere to avoid drag and be travelling fast enough to maintain an orbit at the desired altitude.

They are launched on the top of rockets.

All satellites are launched to space and into their orbit by hitching a ride on a rocket or on the Space Shuttle, where they are placed inside the cargo bay.In order for a satellite to be launched successfully, the launch rocket must be placed in a vertical position initially. This allows the rocket to penetrate the densest layer of the Earth’s atmosphere quickly, which helps reduce fuel consumption.