Might I point you to another section of the forums for info on getting traffic to your store? Affiliating theory, advice and generating traffic is where you will find such info.
I'm not familiar with etsy but there isn't a way to "connect" your zazzle to pinterest. You just have to add your referral code to the end of your links so that Zazzle can know its your personal link and give you the referral for it.
Hover over the round icon on the top right of the home page, between the cart and chat icons and click "my account" from there you'll see 3 tabs, My Account, Associates, Earnings. Click Associates and make sure you're enrolled into the referral program, that is where you will find your personal code.
It will look something like:
https://www.zazzle.com/z/pt91d?rf=238559843123495347The ?rf=238559843123495347 is my own personal referral ID, you must have ?rf= then your own string of numbers on the end of any product, collection or store URL you put anywhere to get a referral royalty.
You can even go a step further and add a tracking code so you know if the links you put up directly leads to a sale, it will look like this:
https://www.zazzle.com/z/pt91d?rf=238559843123495347&tc=Pinterest&tc=Pinterest is the code I use for pinterst, there has to be
&tc= and then whatever text you want to put so you know where it comes from, could be anything, no spaces of course. I hope this helps somewhat, its all stuff I had to read about and teach myself so i'm 99% sure everything is correct.