Decide what kind or kinds of slide rules you want. According to the Sphere Research Corporation website, there are many different types but three basic designs: the full-sized straight or linear slide rule, the circular slide rule and the rarer cylindrical slide rule. According to the book "How to Choose a Slide Rule" by Don Herrold, slide rules can be distinguished by the type of mathematical equations they can be used for. This includes Manheim rules (for basic math and algebra), Polyphase (for power and square root equations) and Polyphase Trig (for trigonometry).
Learn the popular manufacturers. The most popular and widely known slide rule manufacturer is probably Keuffel and Esser, K & E. Others include Pickett, Faber-Castell, Nestler, Geotec, Post and many others.
Check that the sliding function works. All slide rules have some type of sliding mechanism by definition. This piece is called the indicator. A slide rule is nothing if it cannot be operated properly.
Examine the slide rule for damage or wear. Many will have signs of use, unless they are new in the package, which is rare and more expensive. As with any collectible, the slide rule's value is dependent upon its condition.
Purchase your slide rule and begin your collection. Always look for the best quality and build a collection with variety, unless you decide to collect one specific type of slide rule.