Problem :
How do I update a package in Gentoo Linux?
Solution :
This is what you need to read, an intro to portage, the package manager in Gentoo.
To update everything (including dependencies and changes to use flags), then
emerge -avDuN world
To update a single package (again paying attention to dependencies etc):
emerge -avDuN <package-name>
A basic update, without checking for dependency updates would be
emerge -avu <package-name>
The -a means “ask” which is for confirmation, and the -v means “verbose”, to give more info about what it is doing.