Ok. I'm not by any means an expert (read: undergraduate, and it's been a while since I did WWII) but here's how it seems to me. I should also point out that I'm not so clear with the Italians. I'll focus in Germany, and hopefully other kind commenters will help with the areas I miss :)
So. The main British/French response to German aggression in the 30s was the policy of appeasement. Basically, there was '(1) a genuine hatred of war on the part of many who remembered the horrors of World War I, accompanied by a lack of enthusiasm, amidst the depression, for heavy military spending; (2) a a feeling, more common in Great Britain than in France, that perhaps Germany had been death with too harshly in the Versailles treaty and that it's desire for revision was understandable; (3) Hitler's ability to make some Allied statesmen believe he was a reasonable and peace-loving man with limited goals; (4) fear of further Japanese and Italian aggression, which prevented France and Britain from concentrating exclusively in the dangers presented by Germany; and (5) fear of communism and that if Hitler were overthrown in Germany a worse situation might arise: a Communist government'.^1
So, to summarise: Britain and France responded with a policy of appeasement. The main events of the 1930s with regard to that policy:
1933—Hitler becomes Chancellor of Germany
1935—Germany reintroduces conscription, increases size of military.
1936—re militarisation of the Rhineland
1938—anschluss with Austria
1938—Munich Conference regarding the Sudetenland of Czechoslovakia. Sometimes regarded as the peak of appeasement
1939—occupation of Czechoslovakia
March 1939—Neville Chamberlain announces that he and French leaders have agreed to back Poland if it is threatened.
September 1, 1939—Germany invades Poland, Britain and France declare war 2 days later.
The cited source:
Richard Goff, Walter Moss, Janice Terry, Jiu-Hwa Upshur, Michael Shroeder, The Twentieth Century and Beyond: a Brief a Global History, Seventh Edition, New York: McGraw Hill, 2008, p. 246.