To breed your alphas, go to one of their pages and scroll down to "manage my wolf". Click that, then click "breed" and check the box and submit. You then have to wait about 4 days for the pups to be born.
To breed your other wolves, go to the trading post and select male or female, then click the tab 'breeding'. Fill in the rest of the form depending on what you're looking for, then click search. You'll then see a list of males or females up for breeding.
To put your own wolves up for breeding, go to their pages and click "manage your wolf" then "breed". You can set up a breeding fee.
Please note that if you breed your male to someone else's female, they will get the pups. I suggest only breeding your females to other user's males for now so you can build your pack and get the pups.