The German Army's ranking structure and the one of the Waffen SS in the World War II can be a little confusing. Mostly because those structures are different between themselves and are different between America's or British armies.

Here I'll try to show how the hierarchy of the Deutches Heer (army) and the Waffen SS as well as the approximate British equivalent. I'm no British Army expert, so if you find any inaccuracies, please let me know. The America's Army equivalents are similar to the British ones. Note that some of the ranks do not have a clear equivalent.

Equivalency Table (Ascending Order)

Heer (German Army)       Waffen SS                    British Equivalent

Gemeiner(Landser) Schütze Private
Grenadier Sturmmann Lance Corporal
Gefreiter Rottenführer Corporal
Obergefreiter Unterscharführer
Unteroffizier Scharführer Sergeant
Unterfeldwebel Oberscharführer Colour Sergeant
Oberfeldwebel Hauptscharführer Sergeant Major
Stabsfeldwebel Hauptbereitschaftsleiter

Sturmscharführer Warrant Officer
Leutnant Untersturmführer Second Lieutenant
Oberleutnant Obersturmführer First Lieutenant
Hauptmann Hauptsturmführer Captain
Major Sturmbannführer Major
Oberstleutnant Obersturmbannführer Lieutenant Colonel
Oberst Standartenführer Colonel
Oberführer Brigadier
Generalmajor Brigadeführer Major General
Generalleutnant Gruppenführer Lieutenant General
General Obergruppenführer General
Generaloberst Oberstgruppenführer
Generalfeldmarschall Riechsführer-SS Field Marshal

There's also some "sub-ranks" that doesn't go along with the "main line", such as medics (Sanitätssoldat), Staff Sergeants (Unterfeldwebel and Unterwachtmeister), Gunners (Kanonier), Motor Vehicles Drivers (Kraftfahrer) and many others, but, as noted, the ranks above are the main ones.

Phil Stoke's World War II Pages -
Uniforms of the German Military -