How many email addresses total? 2, 3 or ???
If you want just one more, you can just define an additional text field, PrimaryEmail to your contacts table and then add it to the contacts layout. If you want a send mail button for each email address, you'll need to add a button for that and attach it to a script similar to the existing send mail script, but modified to refer to the other email address field. (And if you want to get bit fancy, it's possible to use the same script for both buttons, but pass the email field's name as a script parameter--but that's a more advanced scripting technique than you may be ready to take on at this point.)
If you want to record a flexible number of emails, that can be done, but requires creating a related table of emails (Phone numbers can also be included in this table) with a portal to it placed on the contact details tab. You can add a field to this table you can format as a check box field for designating a primary email address.