Occasionally if you're going to buy a tablet you might have an opportunity to try the tablet out before you purchase it. This is often a case when you're getting the tablet from a friend or purchasing it used.
I highly recommend that you test out the tablet before the purchase. This will save you a lot of headaches and disappointment later on.
For the sake of this discussion I'm going to assume that you're going to bring a laptop with you and use the tablet with that laptop.
Preparation:
Have the applications installed on the laptop that you're going to use with the tablet. I always test with Krita in addition to any other apps.
Depending on the brand of the tablet you're considering purchasing make sure you have the latest drivers for that tablet installed.
Connectivity
Conduct the tests with a wired connection.
Any then verify they work with wireless connection
Drawing
Check if the pen works in all locations on the active area
Check if the pressure smoothly going from zero to 100
Check tilt works in all directions
Check that the pointer generally stays where the tip of the pen is even if you tilt the pen.
Check that location of pen is tracked accurately in over the entire surface of the tablet
Check if all the buttons, dials, work. A quick way to test this is to map the buttons to keypresses. Then you can open a notepad app and press the express keys and see it typing things
Check for stuck or dead pixels
Check for basic color and brightness
All pen displays have more pointer lag than pen tablets. Verify if you are OK with the amount it has.
All pen displays have some minor edge and corner inaccuracy in tracking the pen location. Check this to see how much there is and if you are OK with this.
Verify you are OK with the anti-glare sparkle on the screen. Some people are very sensitive to this.
There should be no cuts or scratches deep enough that you can feel them through the pen
Are you getting replacement nibs with the pen?