Do a demo. By this, I mean demonstrate that you can get work done from home before asking. This may require some unpaid work time on your part, but if this is what you really want, the rewards should be worth it. This also has the benefit of giving you a chance to be sure you like working from home and can be productive there before you go through the effort of asking, setting up a plan, and so forth.
As for doing this demo: Some day when you have to stay home otherwise, go ahead and work while at home. This could be a day when you're dealing with a sick family member, an appliance delivery, utility repairs, severe weather, etc. Alternatively, you could just work on a day you would normally be off work (weekend, holiday).
After having an experimental work from home day, if you still want, you can now go to the boss and say "I accomplished this (<- whatever tasks) while home and found that I could be just as/more productive (<- pick which ever is appropriate) due to being more relaxed/having fewer distractions/more time available/whatever (<- pick as many as apply). If you don't mind, I'd like to work from home more often. Would you mind if I started doing that with whatever (<- desired starting) frequency?"