Choose About this Mac from the Apple menu and check the processor.
If it's a Core Duo Mac, click here, install the DVD, and run Software Update.
If it's a Core 2 Duo or better Mac, follow the Core Duo instructions, and if desired, open the Mac App Store, and try downloading 10.9. If you get told it's incompatible, go to the online Apple Store and order a download code for Lion 10.7.
Mac OS X 10.7 and newer don't support PowerPC software such as Microsoft Office 2004. If you upgrade the OS, back up the computer first.