  Let {(X_i,Y_i)}_{i=1}^n be a sequence of independent bivariate random
vectors. In this paper, we establish a refined Cram\'er type moderate deviation
theorem for the general self-normalized sum \sum_{i=1}^n X_i/(\sum_{i=1}^n
Y_i^2)^{1/2}, which unifies and extends the classical Cram\'er (1938) theorem
and the self-normalized Cram\'er type moderate deviation theorems by Jing, Shao
and Wang (2003) as well as the further refined version by Wang (2011). The
advantage of our result is evidenced through successful applications to weakly
dependent random variables and self-normalized winsorized mean. Specifically,
by applying our new framework on general self-normalized sum, we significantly
improve Cram\'er type moderate deviation theorems for one-dependent random
variables, geometrically \beta-mixing random variables and causal processes
under geometrical moment contraction. As an additional application, we also
derive the Cram\'er type moderate deviation theorems for self-normalized
winsorized mean.
