I do not understand how transistors are used to compute, especially how immense amounts of them are used, how does what know the states of all of them?
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This is a very large, vague, question. The short, somewhat vague, version of the part I know is:
Transistors can act as switches. These transistors can be combined to make gates, such as AND, OR, XOR, as well as flip-flops (registers, to remember things). The gates may use anywhere from 2 transistors to a dozens of transistors for a register.
We can combine these gates and registers to do things like add 2 binary numbers, subtract them, multiply them, compare them, and so on. Creating blocks that do things like this, we can create a CPU (central processing unit, a microprocessor) that can perform computations. (BEGIN: fetch an instruction; decode/compare the instruction; it’s an add, so perform the add; increment the instruction counter; goto BEGIN)
There are levels past this, where you talk about multiple copies of the CPU (multi-core) that operate somewhat independently, or multi-thread, where each core may be doing (kind of) 2 different programs at once, or adding cache memory (more transistors) to speed up the memory access time, or whatever else, because each of these adds more transistors to make it compute faster.
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