Hi Deena,
Love your puppies. I'm new here too and the way I will be going at it is creating a post every day, putting a link to it on Facebook, on twitter, instagram, google+ etc.
Of course this is my personal opinion, I'm sure you will get other ideas and info from more experienced wa members.
You're website looks fine. Here are some ideas of posts I would create (they don't have to be super long posts): A post introducing your pups, names, their character trades, what they like. Silly stuff your dogs might do. etc. I truly believe that every post doesn't have to be about selling, some are just about getting your visitors interested so they come back to see more content.
You should also create a subscription button so that you can get peoples emails, maybe you can set up a monthly newsletter etc.
Or if you have a free ebook with info about dogs, then they get the ebook when they subscribe, something like that. If you don't have a subscribe button then maybe you can offer a little monthly give away,sweepstake (doesn't have to be for something expensive). Set your monthly budget to whatever you are comfortable with, can be a $10 collar, a toy or something.
That way you get peoples emails and you can promote your give away on social media and on your blog.
Once you have a mailing list you can send out an email maybe once or twice a month to promote your website and your affiliate programs etc.
Also I love dogs and I follow a few on instagram because I think they are so cute. Maybe you can get followers by using instagram to post photos of your pets with clever rewarks, links to your posts etc.. Log in to instagram and search dogs and you will get the idea (something like you did on pinterest).
The key also in social media is to be consistent and post at least once a day. You can even schedule your posts by creating a free account on something like Hootsuite (just look it up on google or youtube). I find that youtube has videos on almost everything you can imagine so you can find out how to use hootsuite, instagram etc. there.
I hope this helps and if you need anything please don't hesitate to contact me.
Good luck and don't give up. As the saying goes Rome wasn't built in one day. Keep at it and eventually it will work.
Have a fabulous day.
Paula