What is the process for finding all subspaces of a vector space over a finite field? Specifically, I want to find all the proper subspaces of the vector space $F^2$ over $\mathbb{Z}_3$. the $0$ vector space is the obvious subspace but I find that I have to guess a subspace then check all the criteria to determine if it is in fact a subspace. Also, is there a way to determine the number of subspaces that exist, apriori, or at least a maximum that can exist given the conditions?
Thanks in advance