The statements above about learning how to read the output and to search bugs.gentoo.org and Google will help you fix many problems. Also, the revdep-rebuild utility helps when a new revision of something requires rebuilding dependencies (part of the gentoolkit package). If you're stuck after that, you'll probably need to ask.
Here's an example. I was putting off updates because I was too busy to do much more than check my email and some of the updates were going from tetex to texlive and a new pcre version. The tetex to texlive upgrade requires rebuilding programs like kile and pcre is just a dependency that happened to have a newer version available.
Code:
libtool: link: cannot find the library `/usr/lib64/libpcreposix.la'
make[4]: *** [kile] Error 1
make[4]: Leaving directory `/var/tmp/portage/app-editors/kile-2.0.3-r1/work/kile-2.0.3/src/kile'
make[3]: *** [all-recursive] Error 1
make[3]: Leaving directory `/var/tmp/portage/app-editors/kile-2.0.3-r1/work/kile-2.0.3/src/kile'
make[2]: *** [all-recursive] Error 1
make[2]: Leaving directory `/var/tmp/portage/app-editors/kile-2.0.3-r1/work/kile-2.0.3/src'
make[1]: *** [all-recursive] Error 1
make[1]: Leaving directory `/var/tmp/portage/app-editors/kile-2.0.3-r1/work/kile-2.0.3'
make: *** [all] Error 2
Most of that make stuff isn't relevant (for this purpose anyway). What we care about is the libtool line. A quick Google search for
"cannot find the library" libpcreposix.la (the bold part, quotes included) would probably get you helpful results. However, the output from emerge (Portage messages, not build messages) after the pcre update says pcre no longer installs .la files and to install dev-util/lafilefixer and run it with the --justfixit argument.
In other cases Portage messages will say something useful like a USE flag should be enabled or disabled. The Portage output will have asterisks to the left of the messages. There can be other cases as well, but this is common stuff. I like to send the output from
emerge -uvp to a file before an update so I have a reference of what was updated and what versions were involved.