Pearson's answer is technically correct for smaller satellites, which are flying pickaback as secondary payloads. But it is missing the big primary payloads. So for the sake of completeness, have a look at different Ariane 5 configurations:
Different types of upper section for Ariane 5. Credits: Esa/D.Ducros
A rather common strategy is to 'pile' two or more satellites on top of each other. The upper satellite sits directly inside the payload fairing. Any further satellite below is sitting inside some sort of an inner fairing. The relevant systems for the Ariane 5 are called 'SPELTRA' and 'SYLDA' payload dispensers / dual launch systems.
Depending on the satellites' needs, the upper stage of the rocket (the one directly below the payload dispenser), can be ignited multiple times (it needs to be designed in such a way). This is for instance done with the 4th stage of the Vega rocket. Then, you can deploy the satellites on rather different orbits with only one launch.
For further reading, have a look at the Ariane 5 User's Manual (e.g. page 1-7) or the Vega User's Manual.
However, 'piling' satellites is not the only technique. E.g. Russian Glonass satellites are launched right next to each other, virtually sharing a single payload adapter. This can be done if the satellites are build and designed in such a way, but it is usually not applicable if two totally different customers share a launch of e.g. an Ariane 5.
Proton and Block DM upper stage mounted with 3 Glonass satellites
There are in fact 'user manuals' for virtually all commercially available rocket types and they are freely available. Buying a rocket is a bit like buying a house-hold-device, if you ignore the price tag - they come with manuals. You can google for them, they are amazing reads. There are various implementations for deploying multiple satellites from different rockets / launchers, so it is worth digging for them.