Get a scanner, a shredder and a small file cabinet.
Scan things bills and receipts and organize them into folders. You may want move your bills to paperless so you get an email statement and either pay online or set up direct debit. Then you can just save the emails in a designated folder.
General paper and bills that are more than a year old, shred and get rid of it.
Then organize important paperwork in folders in a single filing cabinet - home purchase documents, important school documents, marriage certificate, birth certificates, warranty paperwork, etc.
On a day-to-day basis, I open the mail when i get home and immediately throw out junk and catalogs that we don't buy from. I open all bills and put the "need to pay these" statements in a basket on the counter. Then twice a month I pay bills. Once a bill is paid I throw the statements into a big box. Every six months I go through the box and either file, scan or shred the stuff in the box.
We never have piles or paper around. It makes me koo-koo!