It sounds like a good approach would be time-series Granger Causality (as mentioned in the comments above). This uses a regression-based approach. Your end result isn't an ontological test of causality, but testing whether one variable helps you predict the other--which is generally what you get from regression. Several time-series texts can help you with this. For example, a new text by Steffensmeier, et al (Time Series Analysis for the Social Sciences, p. 112+) describe this in the context of vector autoregression modelling the same as Enders (Applied Economic Time Series, p. 305+, 4th ed). You are using a simple F-test to (from Steffensmeier), "determine the joint statistical significance of the coefficients on the lags of the variable hypothesized to Granger cause another variable. The null of no Granger causality is equivalent to the hypothesis that all these coefficients are jointly zero" (p. 112).
Enders has a detailed example (310+), using his own research of terrorism. He walks you through the process of creating VAR equations. Much of this process presumes a familiarity with time-series techniques--for example, testing for stationarity, etc, before you can proceed to the actual question you want to answer, i.e., causality. There is also a presumption of some background in linear algebra, since in the example, you need to do a Choleski decomposition. In this case, causality is determined using an impulse response function.
