The core C++ standard and the STL are pretty much cross platform already. Its usually only the GUI and hardware access stuff that requires libraries.
I have used GTK+ as a GUI toolkit and it's pretty good too, although you need to install glib and some other stuff on windows.
RtAudio is nice for cross-platform audio I/O.
The low level networking/sockets stuff is largely the same between windows and linux, you could write a very lightweight layer yourself to handle any differences. I don't have any experience with higher-level networking libraries.
I also like the SFML (simple fast media library) for cross-platform 2d graphics type stuff. It's very nice indeed.
I would suggest, however, that if you are just learning c++ then you're probably better off not looking at Boost (or indeed any of these toolkits) until you've got your head around the basics - by writing a couple of basic console applications, for example.
If you want to learn c++ only so you can do multi-platform dev, be aware that there are many other languages and associated toolkits that may be more suitable, depending on the app you're writing.
Without knowing the type of app you're planning on developing, its hard to say whether C++ (or C or Python or whatever) is the best idea. Personally, I generally turn to Python + PyGTK for crossplatform GUI apps and C# for windows-only apps. You can always plug C/C++ in to replace any components that are running too slowly.