A satellite is only usable while it is above your horizon, so working one is a short, planned event: predict it, point at it, tune for Doppler as it moves, and listen before you talk.
Find the pass with a tracking program or app. It needs your location and the satellite's Keplerian elements (orbit numbers, often distributed as "two-line elements"), and gives rise time, set time, the highest elevation and the direction to point.
Wait for AOS (acquisition of signal), when the satellite clears the horizon. Higher passes are better: a satellite low on the horizon is behind trees and buildings.
Listen on the downlink first, then call.
Stop at LOS (loss of signal).
Doppler: the frequency moves
Same transmitter all the way. Only the motion changes what you receive.
You receiveHigher
Because the satellite is moving at about 7.5 km/s, its signal is raised in frequency while it approaches and lowered while it recedes, and the shift is zero at closest approach. The shift is proportional to frequency; at its largest, near the horizon, it is about 24 parts per million (speed toward you divided by the speed of light):
Shift ≈ frequency × (speed toward you ÷ speed of light). Satellite at 500 km, Earth's rotation ignored. The same pass, three bands.
Pass length11.5 min
Largest shift at 2 m±3.4 kHz
at 70 cm±10.2 kHz
at 23 cm±29.7 kHz
For a satellite at a typical few hundred kilometres, that is about 3 to 4 kHz either way on 2 m, about 10 kHz on 70 cm and about 30 kHz on 23 cm. A narrow SSB or CW signal moves right out of your passband, so you retune a little as the pass goes: start high at AOS and step down. Tracking software can do this for you through CAT control. FM signals are wide enough to tolerate some error, but on 70 cm you still retune in steps.
Power and antennas
A satellite hears you from hundreds or thousands of kilometres away, so you do not need much power, just a decent antenna and a clear view of the sky. A handheld radio with a small hand-aimed directional antenna is enough for FM satellites.
Aim to match the beacon: on a linear transponder, your downlink should be no louder than the satellite's beacon. A stronger uplink steals power from everyone else.
Check your own downlink against the beacon. Too much uplink power blocks others.
Two other effects to know: a tumbling satellite, or the ionosphere, can rotate the polarization of the wave, so a circularly polarized antenna avoids the fades a linear one would suffer; and your own radio's receive and transmit frequencies must each be corrected for Doppler if you want to stay on the same spot on the transponder.