I'm trying to (in priority order):
-read the Bible more
-Pray/talk to God frequently. Remind myself that He is in control
-Be uplifting to others, even when I don't feel it.
-Volunteer to help out in a variety of charities
-Minimize the amount of time on the news (I'm striving for no more than 1 hour/day).
-Listen to uplifting music and watch uplifting movies. Mozart is good, the Rolling Stones notsomuch....

-Exercise
It is easier to talk about not giving into despair than it is to actually do it. I'm fortunate in that I'm retired/semi-retired so I have the time to concentrate on mellowing myself out. If I still had kids in the home or work responsibilities, it would be much harder to avoid worry and become anxious over what is happening, as the world appears to be coming apart at the seams. Knowing that God is in control helps keep me from heeling over too much.