You'll need two browser windows open to TCS for this, one to edit your signature and one for your Cat Page(s).
Step-by-step instructions:
1) Click on "My Profile" in the red bar at the top of the page:

2) Scroll down to "Your Forum Signature" and click "Edit Signature Text":

3) In another browser window, click on "Cat Pages" in the red bar at the top:

4) Enter the user name in the "Search Cat Pages" box and click "Search":

5) Choose the Cat Page you want to include in your signature:

6) Copy the URL from your (Firefox/IE/Chrome/Opera) browser bar. It will read www. then thecatsite.com followed by /a/, then by the name of the Cat Page, e.g. Miezi's Page
7) Go back to your other browser window and type your cat's name or "So-and-so's Page" where you want it in the signature. Highlight it, then click the link icon

Note: You use your mouse to highlight a word: left-click and drag across the word to highlight it, click again. That should put the word in a blue box.

8) Paste the Cat Page URL in the "Enter the destination URL" box and click "OK".

9) Click "Submit" to save your new signature with its link to your Cat Page.