How much sanding do I need to do to refinish a wood floor?
You'll probably want to rent a proper floor sander. A small random-orbit will take ages and you'll probably burn through most of its useful life. 

The sander should come with a variety of paper grits. As with any woodworking project, start with the heaviest and transition to the finest. The final should be somewhere in the 100-120 grit range. 

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How far you need to go depends partly on the stain color--is it markedly different from the current color? Is it dark? Dark stain is more likely to compound if it's not completely removed. You'll see the old stain through the new as dark streaks or patches. 

If you go the route of renting a sander, the work will be easy enough that you can get through the old stain without much effort, and you'll be confident of achieving a good result.