Step 1: Have everyone that sends you bills/statements send them electronically. In other words, stop the flow of any new paper.
Step 2: File statements on your pc and some kind of backup (external drive or cloud service) as they come in.
Step 3: As you have time, scan any paper items you plan on keeping long term (tax returns, for example). The short term stuff, you can either scan or just wait a couple of years, then shred.