The answer to this question comes from my personal experience - I
studied a sociology course at university and the questions we were
given sound very similar to yours!
1) The two classes are the Bourgeoisie (owners of the means of
production - factories etc) and the Proletariat (workers). These two
will forever be in conflict, think the Marxists, because the
proletariat are not seeing enough of the results of their labour!
Basically the idea is that the proletariat are 'alienated' from their
labour, in that they don't own the means of production and are forced
to sell their labour power. The conflict is caused by the proletarians
always wanting more for their work (the Marxist would say they deserve
more for their work) and the bourgeois wanting to exploit them as much
as possible so as to maximise his or her profit.
2) As I've already explained, the bourgeois class own the means of
production within society. This means they own the media, too. They
are the 'dominant class' in that they are the ones doing the
exploiting, and they disseminate their ideology (therefore the
dominant ideology) in the media. False consciousness occurs when the
proletariat start believing what the bourgeois are saying about them -
that they shouldn't unionise, that it's wrong for them to ask for more
pay, etc. You might have seen this occuring in the 'talkback' section
of your local right-ish newspaper. Here in Melbourne, Australia we
have a paper called the Herald Sun, and the 50/50 column is full of
working class people telling other workers to stop going on strike!
I've already discussed alienation a little bit above, but here's a
more comprehensive list of its characteristics: workers do not do the
jobs they enjoy, they work for money rather than love, they don't see
the 'fruits of their labour', they don't get paid proportionately to
the sale price of what they're producing. Crimes arising from
alienation might be theft from work (a baker stealing the cakes he's
made and taking them home), or sabotage of the product (after all, the
worker gets paid no matter whether the bourgeois makes money or not).
Some books and websites you might like to have a look at:
Karl Marx's 'Communist Manifesto' is always good. It's reads like the
propaganda it is, but all the main ideas are there. His 'Capital' is a
fuller (3 volumes) explanation of his ideas, but it's a terrible read
- I don't know anyone who's finished even one volume!
You might also like to look at 'Karl Marx: Selected Writings' which is
edited by David McLellan. You can probably find it in your library,
and you can also buy it here: http://www.oup.co.uk/isbn/0-19-878265-9
(for 19.99 pounds) if it takes your fancy.
A similar title is 'Karl Marx: Selected Writings in Sociology and
Social Philosophy' which again is probably in your library.
If you go to http://www.marxists.org/archive/marx/ you can search the
'Marx and Engels Internet Archive' which has texts online - including
the Communist Manifesto, should you need to take references from it
(and I assume you will).