The easiest scenario is where there is an area nearby that is lower than the bog. Dig a trench between the two and you're done.

If the bog is the lowest point in view, then you would have to fill it in while making a new "low area" somewhere else for the water to collect.

A third option is to spread the low area/bog over a larger surface area. It might dry it out if the low area is made wide enough to absorb more moisture than is draining to it.