If your beats are actually quality, then there are just 2 steps remaining.
Setup An Online Beat Store
It's that easy - that's how you sell beats. Setup a store, upload your beats, and other software will handle the payments part. The harder part is driving traffic and building a presence so that people actually visit your store.
How To Get People To Buy Your Beats
You'll probably want to set yourself up with a YouTube and Soundcloud page. Release your beats here for free, but put in tags (tags are the repeating "purchase this now..." or "your name" bring spoken over the beat). With Soundcloud you can add a "Purchase URL" - set this to be your online beat store, so when people hear your beats, they know where they can purchase the license for them. With YouTube, use the annotation to setup an annotation to drive traffic to your store. Also make sure to include in the video description links to your store as well as other social networks.
Naming Your Beats
Avoid using names like "Reminiscent" - or vague, "artsy" names - instead use names that people would likely search for. When a rapper is looking for a beat, they want to find beats similar to an artist style or to fit a mood. Therefore titles like "Eminem Type Beat - Hardcore, Grime, Inspiration - 'Death'" work best. It's got the tags (of moods), the artists, and the "artsy" name if you want. Make sure to put a good thumbnail - your video can be a static image with the instrumental in the background, or it can be dynamic (ie. changing with the beat)
Where To Find Good Photos For Beat Videos
Unconventional Places To Promote
Self-plug, but if your beats are actually good send them to me by dropping a comment below, and I'll feature it on our site.
Here's an example of it all coming together,