Place the datagrid inside of a layout container that resizes with the window, e.g. Grid, StackPanel, DockPanel, WrapPanel and don't set the height and width properties of the datagrid.
I must admit that if this is giving you trouble, you may want to invest in a good WPF book. I recommend "Pro WPF in C# 2008" from Apress. There's also a VB version, if you'd prefer that language instead.