case

A eurorack case is usually a box with two or more rails, some sort of powersupply and some way to distribute power (e.g. a busboard). A case typically has one or more rows with 3U (Height – 133.4mm) and a certain width meassured in HP (e.g 84 HP). For details on these measurements check out the eurorack construction details site by doepfer.

Commercial solutions

If your time is more valuable than your money, you can go the commercial route and buy yourself a finished case:

The cheapest commercially available case is a Doepfer Minicase. Costs ~85 Euros but doesn't offer too much space and power.
Doepfer offers also bigger cases (e.g. the Low Cost Case LC6 for 310 Euros. Note that this costs 3.5 times more than the Minicase, but offers over 5 times as much space.
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DIY

DIY is the cheapest route but has it's own pitfalls (you can make mistakes, harm yourself or your equipment, waste money and time on things that don't quite work as expected etc.) But if done well you can get a good case for the fraction of the price manufacturers ask for. Use hardware store wood cutting services to get cheap and stable birch multiplex parts for your cases. For details about rails, read the rails article. For details about powersupplies, read the powersupply article.

A small example case can be found here: Minicase