Clockwork Mod 6 is now available for Samsung Galaxy Tab 3 8.0 and as of now, it is fully compatible with SM-T310, SM-T311 and SM-T315. After flashing the CWM, you will gain the ability to flash custom ROM, kernels and whatnot.
1. Get the package from here and place it in the root of your external SD card.
2. Reboot to CWM recovery. Do this by pressing Power+Vol UP.
3. chose zip from sd card
4. Select the root.zip file.
5. reboot and done
You can also use ODIN to flash it.
1. Download ODIN on your computer and unzip it.
2. Power off the device.
3. Restart in “Download Mode” by holding the “HOME” button, “Volume Down” and “Power” all at the same time (for about 5 seconds).
4. Hit the “Volume Up” to enter download mode.
5. Start the ODIN exe program.
6. Connect the device via USB to your computer. Verify the device shows as “Added” in the Message box.
7. Select “PDA” then choose the recovery file you want to flash.
8. Hit “START”
9. Wait for device to restart.