The second chair will be demarcated as the chair of Elijah the Prophet. There is a widely observed custom to set aside a chair for Elijah the Prophet to bear witness to the ceremony, much as we set aside a cup for him at the Passover Seder.
[See other examples of this chair here]
Those who descend from Spanish Jewry, North African and Middle Eastern lands will usually have the table and the Elijah Chair, and will use the Elijah chair twice - first to put the baby on Elijah the Prophet's "lap," and then for the sandak to hold the baby during the bris.
Some have the custom to light candles.
Some set up a dish with dirt in it, so the excised foreskin may be placed in it - a prelude to its being buried shortly after the ceremony.
In different circles (mostly non-Orthodox), where many mohels happen to be physicians and are more used to babies being "out of commission," a circumstraint might be used to contain the baby's movements.
I don't recommend this device.
Others opt to have the baby held on a table for the procedure.
Finally, it is recommended to put a tablecloth on the table and a wastebasket under the table in case there is a need to dispose of any waste-filled diapers, sterile packagings, or used bandages.