Start with Second Tablet on Google Play
What you need to do is to enter the account information on the new tablet.  It should ask you for it (along with the other stuff like the time and date) when you first power the device up.  Alternatively, it will ask you for it when you open up the play store/market app on the device.

There's no need to remove the previous device from your account nor is there any way to.  You can have at least 10 devices associated to the same google account at the same time.

Also, the device will automatically get removed from your account after it hasn't been in contact with the play store for about 9 months.