The data that is send down from the satellites is described in the GPS interface specification document:

GPS interface specification
You'll find the message specification in appendix II (page 65 and beyond).

Parameters of an ionosperic model are transmitted as well, even a single frequency receiver can take it into account. The ionospheric parameters are generated by the control segments and are uploaded to the satellites from the ground stations.

The transmitted time and related synchronization is perhaps the most difficult part to understand.

GPS is based on the accurate measurement of time. The distance between the satellite and the receiver is determined by looking at the time difference between transmission and reception which after multiplying by the speed of light gives the range. In order for this method to work, the receiver clock has to be precisely synchronised to the satellite's clock. The problem is that, in order to do that, one has to know the distance to at least one satellite in order to take account for the effect of the distance traveled by the signal. It is running in circles.

Therefore a slightly different approach is taken. To solve the problem, the mathematical relation between receiver position (lat, lon, h), time offset and the timestamps in the received signals is established. That requires amongst other the almanac and ephimeris data, since these allow the receiver to calculate the positions of the satellites as a function of time.

In order to solve a mathematical problem with four uknowns (lat,lon,h,time), at least 4 independent equations are needed. That is the reason that GPS requires at least 4 satellites to work properly (you can do with 3 if you assume you are at the earth's surface). When the problem is solved, you get lat,lon,h and time all at once.

Note that aviation GPS receivers require at least 5 satellites. The extra satellite is needed for the RAIM function to work; it basically determines whether the extra measurement is in agreements with the rest. If one of the 5 measurements is wrong, there will be no agreement and the receiver will flag a fault.