You are totally possible to achieve a program as same as you mentioned. When you run an Affiliate program, you supply affiliates with banners, links… of your store, products to put them into their sites, forum, and social networks. Every when there is a customer clicking on this referral link to purchase your products (with discount), affiliate will enjoy commission configured in back-end. The process to moderate this Affiliate program is very easy. You could take a look at here.
Can I, easily, set up an affiliate program in my Magento store, so other websites can send customers to my store?
Yes, there are many available Affiliate extensions in the Magento Connect extension marketplace dependent upon how you wish to set up your affiliate program on your Magento store.