While the other two answers are right in saying that the Wikipedia page is a good place to start, a quick summary wouldn't hurt.
First of all you have to understand that there was a massive build up of French troops and military equipment along the French- German border. This border had been massively fortified during the interwar years. The Maginot Line as it was called was a series of bunkers and heavy artillery. To attack it straight on would be suicidal- it would take lots of manpower and careful precesion over a long period of time, at a risk of heavy casualities.
This was not to the advantage to the Germans. Their strength was in their ultra modern armoured corp which was light years ahead of the Allies in 1940, in both technology and tactics. However this meant that their plan had to rely on speed. You've probably heard of Blitzkreig. Therefore they could not afford to get bogged down, especially in areas that you would practically have to lay siege to.
Speed of advance tactics favour flat open spaces with little cases of built up areas. This was the case in the Netherlands and Belgium. In a case of oversight the French had not extended the Maginot Line all the way to the English Channel, giving the Germans a handy weak point to exploit.
Having literally defeated the forces of the Netherlands in a couple of days, and only facing partial resistance from the Belgiums, the armoured spearheads of the advancing Germans were able to encircle around the back of the Maginot Line, and thus the majority of the French Army. The speed of advance, and the lack of any warning caught the French, the Dutch and the Belgians totally off guard, especially the latter two who were supposedly neutral.
Having eliminated any potential heavy troops the Allies had, and having captured hundreds of thousands of troops already the Germans continued to advance into France. Any resistance was crushed by the speed and decisiveness of the Germany Army. Defenses could not be set or held in time, and if they did, they were easily flanked by the greater moblity of the Germans. Although the British landed some troops in North France and Belgium, by the time most of their troops reached the front, yet alone their outclassed heavy equipment, the rest of the Allies were in full retreat. Thus they also had to pull back, otherwise they would have been cut off and captured.
The conquest was swift. it focused mostly in the North and North East of France on flat terrian. The fighting was sporadic as the Germans did not allow any attempts to bring about a frontal battle to succeed. If they had, the German advance could have been slowed down, giving time for more defenses to be made. The German advance was ground breaking in its gain- it literally didn't stop until it had hit Paris and the Channel Ports. We are talking about soldiers in the millions being made prisoners of war here.
Hoped that helped. Sure you can find more detailed info at Wikipedia.