Clarity is key when ordering any kind of booze from a bartender, and while 'neat' is a common word in the world of alcohol, some may not know what it means.
If you order a drink neat, you're ordering a couple of ounces of your stated liquor completely as is — not shaken, not stirred, and not served over ice or with soda water.
A neat drink is a fancy shot of alcohol that you drink slowly. The point of ordering a drink neat is to savor its flavor, so opt for this when you're sampling the good stuff.
Apart from the number of ounces and the type of drink you want, there's no more to say to your barkeep. Your drink will arrive at room temperature with no additions.