How the simulator work?

Recently I focused on how to simulate in classical computer, and I found Qiskit offers qasmsimulator and statevector simulator. And others such as project Q also can simulate on classical computer. So is there a general way to simulate on classical computer? And what are differences among simulators? I mean actually it seems like we just need to multiply gate operation as matrixes.

The second level of simulation is State Vector simulation. In this case, we are basically doing what you mentioned in your question. We take an input state (of size $$2^n$$, where n is the number of qubits) and then apply gates to it through matrix multiplication. Due to the exponential size of the state, this requires resources exponential in the system size to be simulated, and as a result is not considered classically efficient. The only restriction on these simulations is that the gates must all be unitary and all states must be pure.
The last level is Density Matrix simulation. Here, we store the full $$2^n \times 2^n$$ density matrix of the state. As a result we can simulate any quantum channel, and mixed states are permissible. However we now have an even bigger object to work with. These simulations are often necessary for doing work on simulating physical noise or other non-unitary processes, but are extremely limited in size due to their exponential resource requirements.