Tablet not recognized as removable storage
On Android 4.0+ devices, certain devices without a separate memory partition (i.e. separate sd card) don't have the USB Mass Storage option, rather Android now uses MTP (Media Transfer Protocol) or PTP (Picture Transfer Protocol) to transfer files.

NOTE: If your device supports SD Cards, please make sure that an SD card is available in the device before connecting it to the PC.

To configure between MTP and PTP (and USB Mass Storage if an SD card is available): go to Settings > Device > Storage > Menu > USB computer connection.

To transfer files to your device via MTP, make sure it is in the MTP mode, then connect it to your computer via a USB cable.

On Windows: wait for Windows to install the necessary drivers, then your device will be available in My Computer. (more info)

On Mac: You have to install the Android File Transfer software. Follow the steps on this support page.

On Ubuntu: follow the steps in this article.