For example, I am looking for statistics on military conflicts in Africa since the end of World War II.
One way to find datasets in ICPSR is to search it. Keep your search terms simple. I am using just the word: military.
I could then limit my results by geography. In this case, I would limit it to Africa.
Two results look promising.
The codebook, that is, the text of the study is free. To download the data, select the desired format and then log in. For first time users, there is a free registration. Once you have been approved, you can download the data anywhere so long as you are an AU student, faculty or staff.