It will depend if you have Windows Live hotmail or MSN hotmail. For Windows Live:
When you log into hotmail you should see your name in the upper right with "sign out" just below it. Just below that you should see three options. From left to right they are Messenger, options, and a blue circle with a question mark.
If you click the down arrow for options you should see your default language, some themes you can select, more themes, and more options. Select more options and you will get a whole menu. Under "Customize your mail" the 4th option should be "Personal e-mail signature".
I don't have MSN so I had to rely on the interwebs to give me those instrucions. They are:
Select options from the navigator bar.
Go to the "mail' category
Click on the "Personal signature" link.