The basic rules are as follows,
on the set up the competitors thumb knuckles must be showing, both elbows must be on the 7x7 inch pads, shoulders square to the table, hands centred, wrists straight, the non armwrestling hand must be in contact with the peg and remain so during the match, at least 1 foot must be in contact with the floor.
Once the ref is happy, he will give the ready go, you are then free to move into any position you wish providing your elbow remains in contact with the pad, your non armwrestling hand stays in contact with the peg, you have no contact between your shoulder and your arm.
I'm not sure what you mean about pulling under the table, if you mean dropping the body so your shoulder ends up below the line of the table then this is perfectly legal, if however you go below the table and your arm straightens, the match should be stopped due to dangerous position.
There are a load of rules but the best way to see for yourself is to come along to the British championships later this month, the countries best will be in attendance, including all the presidents of the various clubs from around the country who will all be happy to show you around the table.
Hope to see you there,
Dan
Cambridge club president.