Man, a few years ago I could litterally find you just about any album you wanted and have it downloaded with 5 minutes in its entirety just by using the google bar.. those were the PRE sopa days.
Now that that well has dried up. It's not nearly as easy as it once was.
But I used to simply go to google and type " site

file hosting website) and then artist or song title" and results would show up directly as search pages.
Mediafire.com used to be a gold mine but that is all but dried up.
Which sites you may have success searching through google: zippyshare.com (was very good but starting to dry up.)
And sharebeast.com (the latest file hosting site I've come across, have had the most success with this one as of late in regards to searching through google)
So for example>> go to google
>> type in into the search bar " site:sharebeast.com kanye west
>>and boom links from the site for music by ye.
>>if you're looking for an entire album or something specific just add the album or specific song title your looking for.
That all being said, like anything else be carful and use caution when downloading, if you don't feel 100 percent on the link or it looks shady. Don't bother with it, I've never had any sort of issue with this method but I wouldn't advise going and downloading anything and everything that shows up in the search, be cautious of things such as file size in relation to what you are downloading, title of the file, etc.
A decent little site is I also use is hasitleaked.com which posts upcoming albums and newly released albums, the site relays when and often where an album leaks, and where it can be found with a little bit of a Internet scavenger hunt, they don't provide direct links, but provide where a given album can be found with a little search.