This is done with a sink basket wrench from hardware store.
Google search and it will display images.http://www.amazon.com/gp/product/B000BQMKA6
While at hardware store, go look at new sink basket and see how wrench attaches to nut on bottom of sink basket. A hammer and screwdriver are usually not enough, but might loosen the large nut if lucky, but not best plan.
How to: Lay on back under sink, and position mouth and eyes directly beneath sink basket so stuff can fall on face. Then crawl out from under sink and get glasses and flashlight to help see stuff falling in face. Then crawl out from under sink and call neighbor to come over and hold sink basket from top using two screwdrivers down the hole while you twist wrench only to discover you are twisting wrong direction. Have neighbor install 2 new batteries in flashlight while you lay under sink thinking about chiropractor bill. Then while laying on back and facing nut from below, turn sink basket nut counterclockwise and it will come off quickly.
Copy following link for removing garbage disposal sink basket with tips for re-installing tubular drain lines.:http://waterheatertimer.org/How-to-repair-and-install-Garbage-disposal.html#install