The Tabla is actually a set of two drums, the Tabla and the Bayan (or Dugga). The Bayan is placed on the left under the left hand, and the Tabla goes under the right hand. The drums should touch each other, and this point between the drums should be on your body's centreline. Sit in half-lotus position. While this may be uncomfortable at first, the player will find that this position actually keeps the back straighter than plain crossed legs. It means you can play longer and with less back pain... though your foot may fall asleep.
Each drum sits on a cloth ring to keep it stable. The Bayan should be more or less flat, with its head parallel to the ground. The Tabla should be tilted slightly forward, so it is easier for your hand to rest while playing.
I've put together a couple diagrams of the drum heads to better show where given notes are placed.
PLEASE: if you know Devnagari, correct these charts!
The two diagrams
The Dayan (Tabla)
The outside rim of the head is woven rawhide, called the Gajara. The black spot in the middle of the drum is called the Syahi. The syahi is a ball of hide glue, ink, and weight that is pressed onto the drum to improve its resonance.
The Bayan (Dugga)
On the outer edge of the head but inside the Gajira is another ring of rawhide called the Chat. This improves the tensile strength of the threading. The skin itself is called a Maidan. The narrow bit of Maidan showing between the Dugga's offset Syahi and the edge of the drum is the Luv.
And here are some hand placement diagrams for the specific hand positions.
Bayan hand positions
Strike the Luv soundly with tips of both the middle and ring fingers. The heel of the hand should come off the drum to allow resonation, and the fingers should be clawed back towards the palm in a single fluid motion after coming off the strike.
When doing many Ge strikes in succession, they alternate between the basic above and the index finger strike, done the same as above only with the index finger alone.
Slap the hand down onto the drum. This should not resonate. The palm should cover the Syahi.