How do multiple transmitters and single reciever work?
It really depends on how much expense and effort you're prepared to go to to get simultaneous reception of multiple signals.

You can divide your transmission space up in many ways; the most commonly referenced are:


Space Division Multiple Access (SDMA) - separate the space by physical paths
Frequency Division Multiple Access (FDMA) - separate the space by frequency (channel)
Time Division Multiple Access (TDMA) - separate the space by time
Code Division Multiple Access (CDMA) - separate the space by code (this is an implementation of Direct Sequence Spread Spectrum, or DSSS)


If you're any good at visualisation, it may help to think of each multiple access approach as a dimension in the overall transmission space.

Cellular telephony uses a combination of all of these methods (yes, SDMA too - look at a cell tower; they separate the transmission space into sectors using directional antennae). Hardwired networks like Ethernet use SDMA.  Radio stations (music, news, etc) generally use FDMA.  Each approach has advantages and disadvantages; the most obvious disadvantage of CDMA (which is arguably the "best" option) is the cost and complexity.

If you can't afford to do any better than FDMA (which is the absolute minimum you can get away with for radio transmission - don't be transmitting on other people's channels!) then you will need a communications protocol that is collision-tolerant; either transmitters can detect collisions and retransmit, or because it doesn't matter if data doesn't get through.

If you absolutely must get the data through on time then be prepared to spend money on a radio system that will do it.  An FDMA/TDMA combination (e.g. Frequency Hopping Spread Spectrum, or FHSS) is probably the best value for money in terms of cheap-vs-effective; if you can afford radios that do CDMA as well as or instead of TDMA then that would give you the best possible result.