I want to make a site somewhat like http://www.hiphopearly.com/ but how can you upload music like them without breaking the law?
Any site that allows the downloading of material subject to copyright (i.e. music recordings) is in violation of U.S. copyright laws and the web site owner is a contributory infringer subject to liability. So to answer your question - you can't have a site like theirs without breaking the law. Notice their site has no TOS or Privacy Policy, etc. -- A sure sign the site is a fly by night operation.
It does actually have a TOS and a Privacy Policy page, if you scroll to the bottom of the page: http://www.hiphopearly.com/terms http://www.hiphopearly.com/privacy They probably pay some kind of fee towards the record labels, which is why they sell advertising space on the site to cover the costs.
They also have a DMCA policy. Might want to look into that. This is the MP3 generation, a lot of tracks are meant to be shared these days. Especially mixtapes.
Even if they do have a TOS though, it usually means jack all. They can't make their own laws. Stay within the law is my advice!
By ensuring that all material uploaded either has been uploaded with the permission of the copyright holder or that the item is free from copyright. In addition that you have documented and advertised appropriate processes on how to deal with copyrighted materials that are uploaded and you can demonstrate that these are followed. You should still have a good IP lawyer on hand and deep pockets even with these in place