I know the Romans had slingers as a military unit, but even Mr. Google can't tell me much about it. Does anyone know what type of sling they used, what style they used, etc?

http://www.digitalattic.org/home/war/vegetius/index.php#b112

Likely the only truly reliable information you're going to find will come from this book. Otherwise, try images in Roman Sculpture. I don't think there was a regulated pattern, as we would think of it.

Therefrom:

The Sling:

Recruits are to be taught the art of throwing stones both with the hand and sling. The inhabitants of the Balearic Islands are said to have been the inventors of slings, and to have managed them with surprising dexterity, owing to the manner of bringing up their children. The children were not allowed to have their food by their mothers till they had first struck it with their sling. Soldiers, notwithstanding their defensive armor, are often more annoyed by the round stones from the sling than by all the arrows of the enemy. Stones kill without mangling the body, and the contusion is mortal without loss of blood. It is universally known the ancients employed slingers in all their engagements. There is the greater reason for instructing all troops, without exception, in this exercise, as the sling cannot be reckoned any incumbrance, and often is of the greatest service, especially when they are obliged to engage in stony places, to defend a mountain or an eminence, or to repulse an enemy at the attack of a castle or city.

The Romans used mercenary or allied slingers during the Republic, and these would have fought in their own units (for instance, Balearic slingers with Caesar in Gaul), but there are no slinger units attested during the empire. Regular legionaries practised the sling: in addition to Vegetius, mentioned by Woodsj above, the speech of Hadrian to troops at Lambaesis shows horsemen practising slinging (!). It's likely that auxiliaries (non-citizen but regular units) also practised slinging-- the Batavian auxiliaries in the fort at Vetren used emergency, plug-shaped lead bullets during their fight. Barbarian allies or mercenaries or auxiliaries using the sling appear on Trajan's column.

But what did Roman slings look like ? I think a piece of a leather sling might have been found at Vindolanda (a pouch); otherwise-- we don't know.