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The first question is: What is instantaneous speed measured against (that is, what is the “ground” relative to which the speed is measured)? Remember that there is no such thing as absolute speed.

The closest to an absolute speed would be the speed relatively to the cosmic microwave background. That speed would be measured by measuring the Doppler shift in different directions. In the direction you are heading to it is blue shifted, in the opposite direction it is red shifted. The amount of blue/red shift gives you the speed.

However the speed relative to the CMB is probably not the most useful. In particular, since you assume no sort of warp drive or similar, you're surely still in the Milky Way, and indeed probably quite close to the Sun. Probably the more useful measurement would be the speed relative to the interstellar medium (this would be the equivalent to measuring airspeed of an airplane or speed relative to the water for a ship). If you are *very* fast (relativistic speed), you probably encounter enough particles to measure the speed of those atoms directly when they hit your space ship (or whatever shielding you use to prevent them hitting the ship). Otherwise you'll probably resort to the Doppler effect again (either by taking radiation the gases emit naturally, or using a sort of gas radar).

Another possibility is to measure your speed against nearby stars. The movement of the stars is pretty predictable even over centuries; unless you're going to have very long travels, that should be sufficient. Moreover, your destination like is a star anyway, so the movement relative to the stars is ultimately what matters most.  Measuring the speed relative to those stars is done by parallax for tangential velocity and again the Doppler effect for radial velocity.