The first step is to keep awareness of your thoughts and feelings. Next is to remove partiality towards thoughts - you learn to take every thought as is and you learn to not have feelings towards the negative ones. That is you realize that you're partial to negativity - for some it's an excuse or explanation, for others it is deeply engrossed beliefs in certain ideas. Whatever it is you have to realize that you're more gullible to some type of thoughts than others.

Next is evaluating the impact of the thoughts on your real actual life in terms of steps you can take. Often times there isn't anything you can do about those thoughts and you drop'em like hot coal. Sometimes you find you can do things differently or avoid certain circumstances to not let those thoughts recur. Some other times it's a longer term thing. Point is to map thoughts to concrete actions and drop the ones that cause you negativity but have no action possible to counter. In yet another words drop the madness and keep the actions.

Rest is practice - you'll initially fail but so long as you notice it it'll get better the next time. You can also use distraction initially if your thoughts are too overwhelming.

It's a slow process especially for adults but it works!