At the start of the war, the Germans implemented the Schlieffen Plan. They fought through Belgium quickly (they had hoped to be allowed free passage but were not) and then hit France. In the meantime, the French were attacking into Alsace-Lorraine in the South, they had initial success but were then thrown back by counterattacks.
The French, by then joined by the British Expeditionary Force, then concentrated their power in the north to try to stop the German attack that had come in through Belgium and the Ardennes. They were slowly pushed back, but at that point, it became clear that the Schlieffen Plan would not work as implemented. The Germans had not put enough manpower into their attack and their supply lines were stretched and vulnerable.
Once the initial German thrust was stopped, the "race to the sea" ensued. In this process, each army tried to get around the other's flank and advance. This series of flanking maneuvers ended when the armies got near the sea (at the First Battle of Ypres) and winter set in.
From there, things devolved into trench warfare.