I remember when I was new, I almost threw my monitor out of the window in frustration and not understanding things. However I think the previous versions in which I began in were a bit better than the current version.
You will eventually understand how it works if ya play quite often... you just have to realize that the synch isn't too good and what you see on your screen may not be what another player sees on their screen. You said you explode cars and the people are driving in it are still alive... that just means that on your screen their vehicle was more damaged than theirs, so when you kept shooting it exploded on your screen, but on their screen it just got more damaged so they drove off. Usually you will know their car has blown up on both of your screens if they stop while its on fire.
When using a weapon like M4, M60, MP5, try and run around and find a good spot to hit your victim, if you stand straight and just fire while they are, bullets may get cancelled out even though on your screen it looks like its hitting them.
There can also be pretty nasty laggers out there with high ping or slow computers that make it almost impossible to hit them. The best advice I could give you for them would be to just avoid them really.
Anyway I don't want this reply to end up bein a how-to of Deathmatch, but just keep practicin and you will get it... hopefully in the newer versions coming out, it will be easier for us all.