elementary set theory - How to determine cardinality of an infinite set using Aleph numbers?

So I was reading a little bit about cardinal infinities, and I thought it was pretty interesting. However I wanted to know a little bit more about how to use them. For example, how would I determine the cardinality of the set of all real numbers? The one thing I know is that if it is countably infinite, then the cardinality is $\aleph_0$, and if it is uncountably infinite, then the cardinality is $\aleph_n$ ($n>0$). I understand the difference between countable infinity and uncountable infinity, so therefore the difference between between $\aleph_0$ and every other $\aleph$ number. But the problem is that I don't know the difference between any of the uncountable ones. What is the difference between $\aleph_2$ and $\aleph_3$? And how can I determine which $\aleph$ number is the cardinality given any uncountably infinite set?