Acceleration, by definition, is the rate of the change in the velocity (speed). Since it is the rate (changes with respect to time) of speed; it is reported in the units of meters per second square.
So to find this rate (acceleration), you need to find two speed values at two points in time, then simply divide the changes in speed (between the two points) by the time elapsed.
Specifically, record the speed of the vehicle at any point in time (which you like) and as soon as you record the speed, keep track of time. After a certain amount of time, record the speed again.
Now, let's call the speed at the first time-point 'V1' and call the second measured speed 'V2'. Note that V1 is measured at time 1 or 't1' and V2 is measured at time 2 or 't2'.
The acceleration (shown with letter 'a') is then defined as the following: a=(V2-V1)/(t2-t1). In other words, find the change in speed and divide it by the change in time!
You can find 'a' at the time interval and speed range of you choice, i.e., you are free to choose your starting point and ending points at the window you want to get the acceleration.
Most manufacturers report their cars' 0-to-60 mph acceleration, so you can start at time 1 with V1=0 (start from standing situation) and then record the time when you reach 60 mph (V2=60).
In this case, a=60/t where t is the time you reach 60 mph. Please note that you should always obey traffic laws and never violate the laws. Only drive at 60 mph if legally allowed.
Please note that this method can be used for any moving object, provided that you can have it's speed at the two points in time.
Please use extreme caution not to disturb the driver or drive at speeds above the posted speed limits.
Finally, be careful of the units of time and the speed. If you are using mph (miles per hour) your measured time difference should be in hours too.
For example, a 5 minute interval is 1/12 of hour, and for the case of 0-to-60 mph, we have: a=60/(0.083)=722.82 miles per hour square.