Two different "Hitler Youth" groups are being discussed here.
a) With regards to the Hitler Youth Division, they weren't smart soldiers. They fought like tigers, and were well indoctrinated, but they didn't have the sense to withdraw and save themselves when cornered. The classic and most well chronicled example is Buron (see "Bloody Buron", an excellent book by the HLI Association) where elements of SS Panzergrenadierregiment 25 made a stand against the HLI of Canada. While two or three companies of SS were killed or captured almost to a man, while inflicting 262 casualties on the HLI, the tactics of the SS boys left much to be desired. Many would stay in holes and have to be eliminated by point blank 75mm gunfire from the supporting tanks of the Sherbrooke Fusiliers. Casualties for the HLI were high, but it was also their first real battle in Normandy and certainly their first battalion size attack. This was the second week of July.
b) I don't know how the Hitler Youth as a whole fought - referring to the youth movement in Germany - but I suspect they were never formed into their own units. Some HJ boys acted as augmentees, notably in the Berlin fighting, and may have been integrated into local Volkssturm (Militia) units (called the Landsturm in Prussia, incidentally).
The HJ was a paramilitary organization - sometimes better described as "pre-military", and while indoctrination into firearms formed part of their syllabus, I think the HJ dagger was their primary "weapon", and at that not a weapon at all but merely worn for show (possibly also used as a tool on campouts). The HJ concentrated (and there were different branches I believe - Marine HJ, for example, and an air service I think sort of like our Air Cadets) on physical fitness, camping, citizenship....they may have received less militaristic training than our own Army Cadets. I'd have to look at my references to be sure, though.
I don't recall them being renowned for fighting, as Ghost says. German propaganda may have played up their role in the fighting - and they may have been numerically significant in Berlin in 1945; one of Hitler's last public appearances was to decorate an HJ boy with the Iron Cross Second Class for knocking out a Russian tank IIRC.
EDIT - one point to D-n-A (who is right on with his other comments) - the HJ was never mandatory but most youth did serve - you miss the one step before joining the Army, however, and that was that all males were required to serve in the RAD (Reich Labour Service) before the Army. This may have been waived during the war, I'm honestly not sure now. But certainly pre-war and in the early war years it was a requirement.
It was pre-military training as well. While they did manual labour for the state, they also had uniforms, and did drill. See my page at http://www.deutschesoldaten.com/customs/rad.htm for some pictures of what I mean.
