smooth side up. Reason, fibers are more intact for the tension load and the bottom rough surface will hold glue better.
TBIII works, many dont care for it, hide glue is generally better. Reasons, tightbond is waterproof which dleays the drying process of skins, sinew, and wood. Hide glue is made from those items, is chemically related wont hold in moisture like TBIII and allows shrinkage better.
rawhide can be wet or dry, but wet is prefered because you can stretch it allot to preload it ( make it work more for the mass it has ) it shapes better to the back of the bow, and shrinks when it dries ( again working more to make up for its mass ).
wrapping is needed on the ends ( The entire thing is better ) to prevent it from lifting. Most prefere medical gauze as it wicks water for easy breathing and drying. Also wont leave inpressions into the skin once dry.
It can take about a week for it to be completely dry ( it, the glue, and the wood under it needs to dy, not just the skin )
You need to know it makes a mess, have papertowels and have fun