Install (emerge) app-portage/gentoolkit if you don't have it. This package include the utility revdep-rebuild, which we will need.

1. Update the local portage tree
   root# emerge --sync
2. Check for updates in the entire system.
   root# emerge -pvuDN world
   This is equivelant to
   root# emerge --pretend --verbose --update --deep --newuse world
3. If you are ok to update the entire system, do
   root# emerge -vuDN world
   Otherwise, you can choose to update only the packages you want, by doing "emerge -v <package-name>"
4. Check if you have installed any masked packages in the file /etc/portage/package.keywords. Run "emerge -pv <package-name>"  to see if any of those packages have upgrades. If they do, upgrade them as you see fit.
5. Check for packages that are not associated with any explicitly merged packages:
   root# emerge --depclean -pv
6. If you ok to let emerge to take care of clean out the deprecated packages, do
   root# emerge --depclean
   Otherwise you can remove the package one by one by doing "emerge -C package"
7. Fix the broken dependency by doing:
   root# revdep-rebuild
8. Sometimes you may need to run revdep-rebuild a couple more time, till there is no more error.