It'll depend on your niche, how many followers you have on social media, the kind of email list you have, the sites that are likely to promote you, the money you're prepared to spend on advertising. Give us a bit more info and we can help you find the best strategy for the time and money you have available.
The best way to promote your referral links is through search engines an art known as seo (search engine optimization) - you will have to do keyword research and create backlinks.
The quickest way to gain traffic to your affiliate link is by paying for Pay Per Click (PPC) advertisement on search engine like Google /Bing or putting advertisement at some paid to click (PTC) website like Neobux. You may not get quality targeted traffic though so success is all depends on your niche, merchant sales page, and your budget.
If you thought long term and stay able links ,you have to require to consider lots of topics which help you to build standard strategy. PPC costly and effective for shortly referral traffic.