Ground pollution typically stems from your handling of sewage. You are quite limited in your options to handle sewage, but must do so in order for your city to be properly inhabitable. You basically have three options:
Build a sewage outflow pipe. This option produces the highest amount of ground pollution, but is your only option in the early game without taking regional options into account. It should always be built as far away from your populace as possible.
Build a sewage treatment plant. This option is more expensive, but has the capacity to handle sewage treatment for larger cities and is modular. It also cleans the sewage instead of dumping it onto the ground, drastically reducing ground pollution. When one of these are built, all sewage outflow pipes should be demolished. Keep in mind that in order to build this, you will need to have a City Hall with the Department of Utilities module added somewhere in your city or region.
Send sewage to another city in the region that can handle the extra capacity, i.e. a city with a sewage treatment plant. There is a charge for this, but the benefits of getting that pollution out of your hands, and getting the extra development space is well worth it. This option has the most mutual benefit, as it eliminates ground pollution in your city, provides extra revenue for the destination city, and decreases region pollution overall by sending the sewage to an efficient and clean disposal facility.
Once you remove a source of ground pollution, the land will gradually "heal" over time, and become properly inhabitable again without adverse affects. This does take quite some time however, so you should always plan your city around areas you think would probably be uninhabitable.
EDIT: As pointed out by both Chromium and Dude in answers below, Trees will help clean up ground pollution faster.
IMPORTANT : If you exceed the capacity of your sewage treatment system, sewage will begin to back up across your city and cause ground pollution anywhere this failure takes place. If you are experiencing widespread ground pollution outside of your sewage handling facilities, you need more sewage disposal capacity.
Ground pollution is also generated by the low-tech level industry. Again, the best way to deal with it is to upgrade to a tech level that doesn't produce ground pollution by upgrading your education systems.