You can find the Getting Started Sample Application for Delphi 4 and up in:

SAMPLES\Delphi 4-7/GettingStarted

This sample application provides you with a visual application that shows you, method-by-method, property-by-property, how to use the most important features of the library. The application has various tabs, each demonstrating an Xceed Zip method by displaying the most important properties you need to fill out, and providing an action button to run the method.

The methods demonstrated are: Zip, Unzip, TestZipFile, ListZipContents and PreviewFiles.

To use the sample, load the STARTED.DPR project file, then run the program. The application itself explains everything to you on screen and with the help of the yellow pop-up "ToolTip" boxes when you move the mouse over the controls in run mode.