How To Choose A Rear Derailleur
First, narrow your search to models that will fit your bike/drivetrain, then consider other factors like price and weight.
For fit, the factors that are most critical are supported speed (does the derailleur support the speed of your bike's drivetrain, mount type (can it be mounted to your bike), cable pull ratio (is it compatible with the shifters your bike uses and the cable length those shifters pull with each shift), and cage length (is the derailleur long enough to support then cassette/gears you're using).
Assuming you're replacing a rear derailleur, the easiest solution is to replace it with something with the same specs. You can do this by narrowing down the fields mentioned above. Or, search for the derailleur you're looking to replace then click the SBP Link on that page. Clicking that link will take you to a search result for rear derailleurs with the same critical specs.
If you plan to change the size of your rear cassette or front chainrings, you may have other issues to consider such as the total capacity of the cassette.
As a general rule, the large the spread between your smallest and largest rear gear becomes, the larger the rear derailleur cage you'll need to shift through all of those gears while keeping your chain taught. But, you'll have more precise shifting if you choose a derailleur with a cage no longer than you need to handle your drivetrain's needs. Here's some more information about how to calculate this.