Originally Posted by
Ren
When you right-click the .zip file, there should be an option "Extract Here" that extracts the file(s) from the .zip into the current directory.
paint.NET however does not work in Linux by itself as it is a Windows executable program. It would require Windows emulation software such as Wine installed to get it to work, and you would also have to install Microsoft's .NET framework to Wine as well.
If you prefer alternatives without the hassles, I like Pinta for pixel art on Linux distros. It's very similar to paint.NET, and can be found in the Ubuntu software center.