I guess everyone has run into missing dll's issues from time to time. What I am trying to get is the 'recommended' method to find and install the dll's. Finding out which dll's are missing is easy enough using depends.exe.
That depends greatly on which DLLs are missing and why they are missing, I don't know that there is a one-size-fits-all answer.
My advice would be to use depends to find which DLLs are missing, try to find out where those DLLs were supposed to be installed (and what application was supposed to install them), and then try to reinstall that application or find out what happened to screw up the dlls.
Another thing to check is for 32bit/64bit mismatches, that can make it seem like DLLs are missing sometimes, especially on 64bit platforms.
Or if you are using .NET, you can have trouble with assembly versions and the GAC sometimes.
You can also check the PATH environment variable, I would advise against blindly adding to your PATH to get it to find DLLs you want, that can cause all sorts of other weird problems.
Sometimes you have to hack around with the PATH or copy files to get things to work, but it is usually better if you can figure out what went wrong in the first place and fix it.
Get the DLL from its publisher's website, if possible, and then follow the publisher instructions to install. Don't forget to respect licensing rules!
Don't use depends.exe anymore, it hasn't kept up with developments in the Windows core and deployment strategies like the side-by-side cache. Trying to fix the warnings it gives will actually mess up your machine pretty badly. Only use it for hints if a program actually fails to start.
99% of the missing dll errors that I tend to come across are missing C++ runtime libraries (eg =MSVC*.dll=) or the .Net framework, where the developer has built with dynamic linking to the C++ runtimes but hasn't created an installer with the required merge modules, or they have built a debug version which links against the debug runtime libraries which you are not permitted to redistribute.
In the vast majority of these cases, simply installing the correct Visual Studio 2005/2008 C++ runtimes (eg see here) or .Net framework will fix the problem.