Since i am not a monk, neither an expert in Buddhism, my answer will only express what i think that may be the view used by Buddhism.
You can do something good about your negative Karma (see below), but you must know that our Karma cannot simply disapear. You cannot make your Karma go away. As soon you make any action (physical action, verbal action or even toughts) you are already generating Karma. The seeds of that Karma may grow up and take effect right away, a few seconds later, or even days, years or in your next life(s). A very simple and linear example: you call a ugly name to a big and bad guy on the street (you are generating bad Karma), then, as a consquence, the big bad guy will punch in your face and that will hurt a lot (ok, stupid example lol). You suffered the consequence of your bad Karma. Or...you call the name to a guy in the street but he ignores you...who knows, you may suffer the consequences of such bad karma within 5 life times, or within billion years. Maybe you will never suffer because of that: not every action will have time take effect because in the meanwhile you may reach Nirvana for example. Not every action will create a result with meaning, a Karma with significant impact. Maybe calling a bad name to a guy on the street will just make him moan and groan for a little and thats it.
With that in mind, what can you do about bad Karma? Well, since i am a Pure Land Buddhist my answer will be just accordingly to that. You must investigate carefully what other Buddhist Schools have to say. But before that i will tell you first what in general Buddhism says: avoid bad actions! Generate Bodichita as someone said here. Cease all bad toughts. Clean your mind with meditation and have peace with that. Do the precepts and avoid any bad action (verbal or physical) and do good actions. Have a good mind towards every people and every being and wish them (even if they are bad to you) the best. With such actions you will generate good Karma that may counteract a little the bad Karma you may have. Maybe such seeds of good karma may delay the bad ones. But remember that even Buddha (while in the physical form of Shakyamuni Budhha or Siddharta Gautama) could not avoid bad Karma! Thats something to bear in mind: no one will escape to bad (or good) Karma completly until Nirvana.
Now, what you can do according to Pure Land Buddhism is to do Nembutsu: recite the name of Amitabha Buddha with a single mind.
Doing recitation will rippen away thousands of seeds of bad Karma. It is said that recitation can stop (so to say) the Karma of previous lifes aeons ago.
You can read about that here page 402 [the printed page on the ebook itself is the 382]:http://www.buddhanet.net/pdf_file/budglossary.pdf
There you can read:"All evil karma results, ultimately, from delusion, the antithesis of
enlightenment. Such practice as Buddha Recitation leads ultimately
to enlightenment and thus dissolves away evil karma. It is as though
a house were boarded up for ten thousand years. As soon as a window
is opened, eons of darkness disappear in a split second.
By sincerely invoking Amitabha Buddha’s name, which is
in reality identical with Amitabha himself, we identify ourselves with
Amitabha. As a result of this identification, a portion of his merits
is transferred to us. These merits, which are now ours, are sufficient
not only to counterbalance the effects of our evil actions but also
to ensure our rebirth in the Pure Land. The law of karma has not
been suspended for our benefit. All that has happened is that a more
powerful karma has cancelled out one that was weaker."
Hope that this was useful for you