The fastest way to get this item on Battle.net is via trading, you can use the Item Price Checker to see how much Trang-Oul's Guise is worth.
Farming it by killing monsters is possible, check the drop rate table below for more information.
It can also be gambled but the chances are very slim.
Trang-Oul's Guise drop rate table
The monster with the highest drop chance of dropping Trang-Oul's Guise is Baal on Hell difficulty in The Worldstone Chamber of Act 5. Farming the monsters listed below gives you the highest chance of finding that item.
Trang-Oul's Guise variants
Below is a list with different variants of Trang-Oul's Guise. See the stats of its normal or upgraded variant.