Ubuntu will read most memory cards, USB thumb drives, CDs, DVDs, and floppy disks with no difficulty. It will even try to mount automatically any Windows partitions it finds on the same machine. Note, however, that this doesn't work both ways: If you're dual-booting to Windows or Mac OS X, the other OS won't be able to read your Linux partitions without additional software.
Ubuntu can also connect to Windows network shares from the Network Browser, which you bring up by choosing Network from the Places menu. You can access other types of network servers--including FTP sites and WebDAV shares--by choosing Connect to Server.
If cross-platform compatibility is your goal, it's important to pay attention to file formats when creating documents on Linux. For example, by default the OpenOffice.org productivity applications will save documents in OpenDocument format (ODF), which Microsoft Office can't read at the time of this writing. You'll need to specify the Microsoft Office format from the Save dialog box if you want to share files with your Windows-bound friends and coworkers.
Occasionally you may encounter a certain Windows application for which no Linux equivalent exists, and that you simply can't live without. In such cases a software package called Wine--available through the Synaptic Package Manager--can sometimes help. Wine is an emulation layer that lets you run native Windows software in Linux. It doesn't work for every application, but the list of supported programs is always growing.
Obviously this guide is just the tip of the iceberg when it comes to the wide world of Ubuntu and Linux computing. We'll keep updating this and other articles as Ubuntu continues to evolve, but if you're still stumped for now, your best option for further assistance is the Ubuntu forums, where beginners and advanced users gather to troubleshoot (and just shoot the breeze about) their favorite OS.
If you ask for help with a particularly thorny technical issue, you may be asked to post the contents of system logs or configuration files to help the gurus diagnose your problem. That may even involve delving into the dreaded world of the Linux command line (which you can access via the Terminal, under the Accessories heading of the Applications menu). Don't be afraid! Just follow any instructions you're given, but pay attention--the more you learn about Ubuntu, the closer you climb to guru status yourself.
Above all, have a good time. Linux's greatest strength is the community around it, and by choosing Ubuntu you have joined a thriving, growing community of users of one of the most powerful and exciting operating systems available today.