A few words on file types are in order. You should be aware that not all format of files can be re-loaded into Dia after saving and that most supported file formats lose information to some degree.
The only format guaranteed to be lossless is Dia XML. Happily, you are unlikely to accidentally save in a lossy format because File->Save always produces a file in Dia XML format.
Files in Dia XML format are automatically compressed using gzip to save disk space. This is almost necessary since, without compression, even simple diagrams are very large because they store much redundant information. Because Dia XML files are already compressed, you should not try to compress them manually—it will not help.
Dia supports exporting to many other types of file, such as:
Computer Graphics Metafile
HPGL
EPS
PNG
SVG
TeX
WPG
To create a file in one of these formats, select File->Open... from the Main Popup Menu. Choose a name and the desired format in the resulting dialog, which works like a save dialog. An appropriate file extension is automatically added.