From Chanticleer Society

Spirit + Citrus Juice (lime) + Sweetener + Soda in an ice filled glass

Along the same lines as a Collins, the main difference in a Rickey is that it is always made with lime juice instead of lemon. A Rickey is thus made by stirring a spirit, sweetener, and lime juice to an ice filled glass, and then topping with soda water.

For an example, see: