How was france and britain able to make the agreement with germany without czechoslovakia being involved? And how was the reaction of the public in the affected countries?
This question is especially interesting because in May of 1938, in the wake of the Anschluss of Austria*, the Czechoslovak army began mobilizing after Hitler (through Sudeten-German leader and Hitler lackey Konrad Heinlein) demanded autonomy for the Sudeten Germans and Britain and France advised Czechoslovak leader Edvard Benes to concede to the demand. This put Britain and France in a frightening position, as Czechoslovak maintained a military alliance with France specifically aimed at countering German aggression. Britain and France did not want to get drawn into a war with Germany, especially over "far away people of whom we know nothing" in Czechoslovakia (as Neville Chamberlain later said of the Czechoslovaks), and even favored Hitler's demands for Germany autonomy in Czechoslovakia. The Western Powers warned Benes that France was not prepared to honor its alliance, and Benes backed down and agreed to participate in further negotiations.
You may be aware of all of this and it may seem off topic, but it very much relates to your question because of its relation to this second question: what happened between May, when Czechoslovakia mobilized its army to defend against German aggression, and September, when Benes reluctantly conceded to the Munich Agreement and chose not to resist in any way? In summary, the British and French leaders and diplomats (especially the British, who steered French foreign policy at the time) threatened to renege on the French alliance with Czechoslovakia if Benes did not play along with the ongoing negotiations with Hitler regarding the Sudeten. The British would demand that the Czechoslovaks agree to Heinlein's demands regarding Sudeten autonomy, and after the Czechoslovaks agreed, the British would then make new demands after Heinlein declared that it was not enough (it turns out that Heinlein had been instructed by Hitler to make unreasonable demands of the Czechslovaks and to never accept a peaceful solution, which makes the British insistence that the Czechoslovaks meet his ever-increasing demands that much more odd). In the days before Munich, Benes even agreed to meet nearly all the demands that would later be found in the Munich Agreement as the British had demanded, and this was still not enough. Benes (or was it one of his diplomats?) later said that the British were treating Prague more like a colonial capital than the capital of a European ally.
When Chamberlain met with Hitler at Munich in late September, Benes's spirit had already been crushed. He had already agreed to full autonomy for the Sudeten Germans, which would have undermined Czechoslovakia's national democracy, and the full annexation of the Sudeten region was just one more step. After Munich, the British told Benes that he had to either adhere to the Munich Agreement or face a German invasion alone. And by then, the Czechoslovak military position had weakened since May -- German troops now stood on the Austrian border as well as the German border, and Poland and Hungary had set their sights on annexation portions of Czechoslovakia, leaving Benes's nation surrounded. The already-compromised Benes chose not to subject his nation to a war that it could not win alone, accepted the terms of the Munich Agreement, and resigned.
Edit: If you are interested in the details, you should read Igor Lukes's Czechoslovakia between Stalin and Hitler: The Diplomacy of Edvard Benes in the 1930s (1996), published by Oxford University Press. Yes, it relies heavily on Czechoslovak perspectives in its analysis, but it seems that the Czechoslovak perspective is exactly what you are interested in.
*As always, I link for those unfamiliar with the term, and am NOT claiming Wikipedia as the source for my argument.
Simply put, the Czech's were left out of the equation. No one bothered about it other than the Czech's themselves.