Amazon's affiliate program is relatively simple. You sign up, put a link on your website, and you'll get money. There are several handy features, such as building slideshows of different products, and the ability to view your earnings online. You can have banners on your websites, or even just simple pictures of the product you are endorsing. Using the aStore setup tool, you can actually create a professional online store, offering products from Amazon.
In 2013 Darren Rowse, a blogger, wrote an article describing his experience with Amazon's affiliate program. (At 2:55 am!) As far as I can tell, his blog is about blogging, and seems to be very professional. Anyways, in the last 10 years, he's made about $420,000, most of it in the last 5-6 years. The main reason he offers for most people giving up on Amazon is that the commissions are too small. (after a google search, I agree: most people complaining about it are complaining about the commission size). However, the one that I would really find annoying is that the cookie stops working after 24 hours. That seems to tell me that, until I have a loyal audience, there is absolutely no point in me signing up.
However, Amazon is a trusted brand. Everyone knows Amazon, and are more likely to buy something from them than anyone else. You can promote high value products to get higher commissions. And, when people navigate to Amazon through your link you get a commission on whatever they buy, so that can end up being more than you expect.
What about Linkshare/Rakuten? First question in my mind: why did they change the name? Apparently some Japanese company took over Linkshare and changed the name. But Rakuten is much harder to pronounce! Anyways, Rakuten seems to be all about working with their advertisers to help find the right connections. Unlike Amazon, Rakuten isn't selling products themselves. Instead, they are making connections between companies wanting to advertise and people wanting to make money from advertising. They offer a lot of data tracking tools and personalized marketing advise.