What is the correct way to put a helmet on? I hear often claims similar to "many cyclists wear their helmets the wrong way" and "wearing a helmet incorrectly significantly reduces it's protective ability".

My helmet is similar to the following one(only with vent holes). Note the two-stage straps on both sides (that is, one can tighten the helmet forward-up and backwards-up).

The manual featured a couple of crossed out pictures - don't tilt the helmet over your eyes (duh!) and don't tilt it so far back, that the forehead is bare.

I am in doubt if I am using my helmet correctly. What are the checkpoints to cover, before being positive that the helmet is not providing just a false sense of security?

For example, tightening. How tight should the helmet be? Must it resist grabbing it by hand and forcing it sideways around my head? 

Another question of particular interest to me concerns the rear straps. Those seem to either hang (very) loose, or, if I tighten them and when I tilt my head (slightly) forward, stretch out and limit the movement (in an uncomfortable way).
The manual pretty much sums it up. The helmet should sit naturally at the correct place without the straps. The straps are only there to hold it in place in a prang, when a bit of chaffing / bruising  is the least of your problems.  A small amount of slack (you should be able to fit two - three fingers between the strap and you) is best. If the straps are pulling the helmet out of position, loosen them.  

Be aware that not all of us have the same sized and shaped heads, so it is possible your helmet is just not a good fit.

Note also the bike helmet only protects against brain injury. Theres plenty of scope for a large amount of pain and cosmetic damage - think what a face plant at 30mph would do, and still scope for massive brain injury with a properly fitting helmet. 

Its a reasonable argument that wearing a helmet provide a false sense of security - essentially if you would not do it without a helmet, don't do it.  

Your helmet is a very last resort -  a "get out of jail" card that only works sometimes. Worth wearing? - I have a mate with a brain injury (non cycling) ... need I say more.....