When you act abominably, you do something really terrible to someone else. When politicians lie, they are behaving abominably.
You can use the adverb abominably to describe anything that's done badly, whether it's truly hateful or simply careless. If a football team loses 0-72, it played abominably, and if a parent abuses her child, she treats the child abominably. At the root of abominably is the adjective abominable, which comes from the the Late Latin abominabilis, "deserving abhorrence." It used to be mistakenly spelled "abhominable" from a belief that its origin included the Latin homine, or "human."