Capitalist class (bourgeoisie) = in a capitalist society, those rich enough that they don't have to sell their labor to live (Rockefellers, Hiltons, Fords, Waltons, Bill Gates, etc.)
Working class (proletariat) = those who have to sell our labor to survive but whose jobs do not give them the power to hire or fire.
Techno-managerial class: Has power over workers (usually including the power to hire & fire) but they still have to sell their labor to live. Middle management & the like.
Lumpen-proletariat class = unemployed, homeless, etc.
Petty bourgeoisie (small capitalists) = small business owners
Slave class = those who are owned by other humans (masters)
Master class = those who own other humans
There were other classes in the past (like Nobles), but they no longer exist. Individuals who are dependant on someone else for survival (children, etc.) are part of that person's class. Class is economic hierarchy. Of course, class is a social relationship and so there are cases where someone won't fit perfectly into these categories and the boundary lines between classes can sometimes be blurry. In addition, there is usually stratification within each of the classes, some workers have better jobs then others, etc. but most members have similar socio-economic relations to other members and so the generalization is justified. Class is not primarily about education, although education does correlate with class (capitalists get "better" educations than workers, lumpens, etc.).