A great deal of what Marx himself wrote about was quite accurate. His "Precapitalist Economic Formations" of the Grundrisse tells a vivid story of a past that is no fantasy. That is not to say, for example, that a good deal of the Communist Manifesto is without flaws, but I think it a bit unfair to say the hallmark of Marxism is that it tells us of "a past that didn't happen".
> ... And why or how should
>they think they are being exploited? ...
Capitalism is a system based upon the exploitation of labor. Without the exploitation of labor, the system literally would not, could not, exist. Workers should recognize this by merely uttering the words "I am a worker".
To get a concrete grasp of this, you must understand not only what exploitation means (all other things equal, a person is exploited if they must labor more than the average amount people work in the economy) but also the relationship between inegalitarian distribution of resources ("capital") and the potential for exploitation.
Unequal distribution of resources allows some to hire others to work for them, to produce profit for them. This is exploitation, and it is also the very definition of a working capitalist economy. Note that exploitation need not mean horrific working conditions, etc. --- it is something quite specific, and quite simple...
Bill