How do you remove chlorine from drinking water?

If you don't want to get into adding chemicals, etc., you can actually just leave the water out for 24 hours and the chlorine evaporates out of the the water. That's a useful process when filling a fish bowl/tank as well (though many hobbyists simply add chemicals to neutralize a number of harmful elements).

Or you could just stick a piece of paper in it for one hour and it will collect the chlorine out of your water.

Another highly reliable method is to use an activated carbon filter.

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Sunlight will break it down and disperse it quite rapidly - but you shouldn't normally be able to taste the chlorine.