For the initial window: Right click on the Internet Explorer icon on your taskbar and click Properties. In the Run field, choose the maximised option. Click Apply then OK.
To maximise new windows: In the existing Internet Explorer Window, Right click on a link and click Open in New Window. After you have opened the new window, close the original (and any other IE windows except the new one). Resize the new window (drag the edges) to the largest possible size, then close that window. Now reload IE and try opening a new window.