How do I edit PDF files with Pages?

You cannot. No application can make any substantial modifications to PDF files - not even Adobe Acrobat from Adobe, who created them. The main purpose of PDF files is to print them. PDF is the end station.

You can import PDF files, like you can import images, but you cannot open them.

You can extract data from some PDF files in a few different ways.

The most obvious one is to simply copy the content from the PDF to Pages.

In some cases you may want to keep the layout of the pictures, and in that case a screen shot may be better. To make a screen shot hold down command-shift-4 and drag the mouse over the area you want. If you want high resolution, you need to increase the zoom the PDF is displayed in.

If you use the free Adobe Reader, you can export the text using File > Save as Text. No formatting and no pictures will be exported.

If you invest in Adobe Acrobat Pro, you get some more export options: HTML, JPeg, RTF, Word document, XML and others, and the result is sometimes acceptable. There is even a menu option to export just the images: Advanced > Export all images.

If you export to RTF, remember that Pages cannot render pictures in RTF files, so you will have to open it in another application like MS Word or NeoOffice.

Also note that there are PDF files that are locked, so you cannot extract any data from those files with any legal program. This is often the case with e-books for example, but also other material where the authors want to protect their copyright.