Sooner or later, we all run into software problems. Some are easy to cure, and some will drive you right up the wall. I can give you my own troubleshooting steps.
If a program is not responding properly, try quitting and then relaunching it. It's surprising that something that simple will work, but it often is all that is needed. At the same time, be sure the caps lock key is not engaged. If that doesn't work, try restarting the computer.
If a program will not open and gives the old "bounce once in the dock and quit" routine, it may be a corrupt preference file or a missing component. Unfortunately, preferences can be in the main library folder and also the user library folder. Where to check first? This is where a second, clean identity comes in handy. Switch to a different user identity and see if you have the same problem. If the problem goes away, it's probably a corrupt preference in your home directory preference folder. Look for something in that folder with the name of the program that ends with '.plist.' Move it to the desktop, then try to start the program again. With luck, the problem will disappear.
If the problem occurs in a different identity, try looking for an associated '.plist' file in the main Library > Preferences folder. If trashing that preference file doesn't help, the easiest thing will probably be to reinstall the program. If you have used an uninstaller to get rid of something else, it may have inadvertently trashed a component needed by your problem child.
If you reinstall and still have a problem, then you could have a conflict. Have you installed any new software? New fonts? If you don't have a font utility, use Font Book to check the validity of your active fonts. Microsoft Word and Excel are especially touchy about corrupt fonts, even if you never use those fonts. And be very careful disabling fonts that you are sure you don't need. Some programs will not run without specific fonts being active.
Check for updates to your problem application. It could be that the latest operating system update caused a conflict. If you just updated the problem program, it's possible that the updater didn't run completely. Try applying the update again. And for what it's worth, I generally wait to apply updates until they've been out a couple of days. I've seen too many updates released and then withdrawn within 24 hours due to problems.
When running system updates/upgrades, play it safe by doing a fresh backup first. System updates have been known to go awry, whether from software errors or power interruptions or a dozen other things. If something goes wrong, you can always start up from that freshly cloned backup and roll your system back to what it was before you started. Professor Carson is not the only one who harps on backups. A fresh backup can save many hours of frustration, and a bootable cloned backup can have you up and running immediately if needed.
If these hints don't solve your problem, remember the MacGroup iBBS and the Apple Support Forums. Mac people are always willing to help others.