Here's my basic understanding of the GPS system. The Russian and European systems, I have no idea, but I imagine the principles must be similar.
A minimum 5 GPS satellites are visible at any location at any time but often more.
A minimum of 4 signals are required for a 3D position fix, lateral position is more accurate than vertical due to the geometry involved.
5 signals are required for RAIM. This allows for one signal to be eliminated from the navigation solution if a gross error results when using it compared to using the other signals. Important point to remember : No RAIM = No guarantee of accuracy whatsoever.
WAAS/GBAS is also used for approaches, but that's an extra subject...
Distance = speed x time so,
Distance satellite to receiver = radio speed x time from satellite to receiver
Knowing the exact transmission time and exact reception time allows determination of signal travel time and therefore calculation of distance from the satellite to the receiver at the time of reception.
Receiver location is the intersection of the 4+ spherical distance lines calculated from the signals using satellite position (see below) plus a bit of trigonometry and the WGS84 global reference co-ordinate standard.
Every satellite transmits 2 signals;
L1 carrier: This is modulated with a data package containing the satellite ID, the satellite "ephemeris" (basically it's current orbital position above the surface) and exact transmission time from the onboard atomic clock. Also a "pseudo random" binary code ( "P" code) which is used to align the clock in the receiver nav unit with the onboard satellite clock therefore allowing determination of the signal travel time. This code isn't really random, it can't be because the receiver needs to know it too in order to "shift" it's internal clock time to match the satellite. It just looks random because it takes a very long time to repeat.
L2 carrier: This transmits the "P" code only but on a significantly different frequency. This allows a correction to be computed in the receiver to compensate for atmospheric delays to the signal from each satellite, enhancing accuracy.
There is a correction for the effects of relativity too. The satellites in orbit are in a weaker gravitational field, therefore causing the onboard clocks to run a bit faster and also at the speed required for orbit the clocks run a bit slower, so to correct for this and to synchronise all the clocks exactly, which is essential for the system to work, there is an update signal from a ground "master clock" once per 24 hours.
Hope that is helpful in some way!