After Hitler and the Nazi party came to power in January 1933, Hitler proceeded to do many things in violation of the Treaty of Versailles, drawn up after the first world war. The first of these was the formation of of the Luftwaffe, and the introduction of conscription, and at that point the League of Nations countries could have stepped in and stopped Hitler. However they stood back and effectively did nothing, as they did when Hitler remilitarized the Rhineland, and even invaded Czechoslovakia and annexed Austria. This policy of standing back and doing nothing was called appeasement, and there were many reasons why Britain and other countries followed it.
The first thing that has to be understood is that the policy of appeasement was not seen as giving in to the enemy as it is nowadays. liveforever points out that it was Chamberlain himself who called his policy appeasement, and he certainly did not see it as a weak strategy. It was a legitimate policy that aimed to bring peace to Europe. At this time, everyone was keen to avoid another conflict, especially one that might entail aerial bombing and poison gas. Even in the Oxford Union, the side debating they they would not fight for king and country won their debate. Even if Britain did want to take action by going to war to stop Hitler, she could not, because she was not ready. British rearmament was taking place, but would not be complete until at least 1939, perhaps later because the depression was having an effect on Britain's economy.
There was also a common opinion that the Treaty of Versailles had treated Germany harshly, and needed revision. One of the major principles that the treaty supported was national self-determination, but Germany was denied this right for the simple reason that if it was allowed, she might end up with more land that she had before the war. Therefore, when Hitler took over Austria and the Sudetenland, many people felt that this should be allowed to happen because the people who joined Germany were Germans. Hitler helped this sympathy along by proclaiming that he wanted peace, and was only defending himself against possible aggressors. He also claimed that he was providing a barrier against Bolshevism, and that Britain and France should be pleased that he was rearming because it meant that they would be protected against communism.
All of these factors, added to the fact that Britain had an empire to protect against the belligerent Japan in the East and would find it had to fight on two fronts, helped to persuade Chamberlain that appeasement was the best policy to follow, and that perhaps if he gave in to some of Hitler's demands he would be happy, and there would be peace in Europe. In fact, Hitler was not the only leader that Chamberlain appeased. When Mussolini invaded Ethiopia in October 1935 Britain condemned the invasion, but did nothing to stop it. This time it was because they did not want to push Mussolini towards Hitler, scared that they might form an alliance. So the British stood back and did nothing while Ethiopia was invaded.
At first, appeasement was probably a good idea. After all, most other countries had an army and air force, and when Hitler remilitarized the Rhineland he was only "going into his own back garden" as Lord Lothian put it. Even when he annexed Austria, he was only following the idea of national self-determination. However, always giving Hitler what he wanted gave a bad impression to him, it made him believe that Britain was weak, and would never intervene, so he could do what he liked in Europe. This was, in effect, the signal that England was giving. Therefore I believe that Chamberlain should have made it much clearer that Britain would intervene if Germany overstepped the mark, and I believe that the mark should have been, at the very latest, when Hitler started moving the goalpoasts over Czechoslovakia, claiming more land than he had previously. This should have made it obvious to Chamberlain that Hitler was not a man of his word, was not to be trusted, and that Britain should intervene both in the interests of international security, and herself.