First, the times are going to be short. If a satellite were right overhead the travel time would be something like 0.06 seconds. So we're going to need some really precise clocks. On the satellite side, timing is almost perfect because they have incredibly precise atomic clocks on board. Both the satellite and the receiver need to be able to precisely synchronize accurate timing is the key to measuring distance to satellites.
Satellites are accurate because they have atomic clocks on board.
Receiver clocks don't have to be too accurate because an extra satellite range measurement can remove errors. On the ground all GPS receivers have an almanac programmed into their computers that tells them where in the sky each satellite is, moment by moment. The basic orbits are quite exact but just to make things perfect the GPS satellites are constantly monitored by the Department of Defense. They use very precise radar to check each satellite's exact altitude, position and speed. The errors are usually very slight but if you want great accuracy they must be taken into account.