Given that the osu!tablet is a two-unit solution (ie: tablet and pen), it can be difficult to tell which unit is experiencing issues when things go wrong. To find out, perform the following steps:
For the tablet unit:
Safely remove the device from your system, and unplug the cable.
Gently plug the cable into a USB slot on your system.
If the tablet is functioning, the light slot on the face of the tablet will flash green momentarily then fall dark. This is normal behaviour.
If the tablet's light does not flash, try using a different USB cable - the ones included with the tablet can sometimes be damaged during transit or after extensive use.
For the pen unit:
Unscrew the grip from the body of the pen, exposing the battery on the inside.
Remove the AAA battery from the pen.
Replace the battery with a brand new AAA battery. Verify that the battery functions in another device first.
Ensure that the battery's positive and negative ends are appropriate in the pen. There are markers on the device that display marks telling you which end goes where.
Screw the grip back onto the pen.
Depress the button on the back end (eraser end) of the pen until it clicks.
If your tablet unit is functioning properly, placing the pen near the tablet will make the cursor on your screen move. If this does not occur and you have followed the tablet verification steps listed above this section, then it is possible that your pen is broken or faulty.
This is copypasted from osu!'s help center article about figuring out if your tablet or pen is broken. Follow these steps and see if any resolve your issue.
If none of these steps help, There is a good chance your tablet is faulty, and you will need to contact Huion or whoever the vedor is you bought it from. DO NOT email osu! as this isn't the official osu! tablet.