Most of the time, an 802.11 ("Wi-Fi") card will find networks by doing what's known as an "active scan". In an active scan, it tunes its radio to each channel it supports and transmits an 802.11 "Probe Request" packet, then stays on the channel for a few more milliseconds to receive "Probe Response" packets from any APs (Access Points -- the technical name for what most people call "wireless routers") on that channel. Because you can usually expect to receive all the Probe Responses you're going to receive within 40ms, cards can scan multiple channels very quickly.
In some cases, a card may choose to do a "passive scan" where it tunes to each channel and doesn't transmit anything, just listens for any Beacon frame transmissions from any APs on each channel. Listening for beacons can be time consuming because beacons are usually spaced 100ms apart, and could be even farther apart. So it can take more than twice as long to do a passive scan than to do an active scan.
In some regulatory environments, some channels have to be handled specially because they are not allowed to be used for Wi-Fi if there is a local radar installation using that channel. On those "radar channels", you must at least start out passively listening, but as soon as you see a Wi-Fi beacon from any AP on the channel you can assume there's no radar present and switch to an active scan.
Contrary to popular belief, passive scans are not the primary kind of scans (active scans are far more common). So although beacons also happen to be what make the AP findable in passive scans, the primary purpose of beacons is to coordinate timers between the AP and the clients, and to notify clients in power save mode that the AP has queued up packets for them (or that the AP is about to transmit queued up multicast/broadcast packets).