A quick summary:
On [July] 29th, Austrian troops began shelling Belgrade, just across the river Danube from Hungary. That same day, Russia began a partial mobilization of its armies, and Germany and Britain began taking military precautions: Germany began to mobilize its navy, and Britain’s navy in the North Sea went to its battle stations.
Also on the 29th, [Kaiser] Wilhelm received word from his bother, Prince Henry of Prussia, that Britain’s King George had told him that Britain would remain neutral. In France, Viviani wished to counsel Russia to restrain itself, to give Germany no pretext for going to war.
By all accounts, July 29, 1914, was a trying day for Tsar Nicholas II. After sending a telegram to the Kaiser at one in the morning, the Tsar received a telegram the Kaiser had sent around 1:45 am, clearly before receipt of the Tsar’s initial telegram, wherein the Kaiser stated he was pressuring the Austrians to “deal straightly to arrive to a satisfactory understanding with you.”
That sentiment notwithstanding, the Tsar had to decide whether he would order general or partial mobilization of Russia’s army. To issue either order would almost certainly mean a general war (Russian mobilization, partial or otherwise, would lead to Austrian mobilization, which would require Germany to mobilize: the need to strike first would almost certainly trump a cautious “wait and see after mobilization” attitude).
Sometime in the early morning, the Tsar ordered general mobilization to begin on June 30th. His advisors were in agreement that either partial or general mobilization would trigger Austrian and German mobilization, so it made no sense to take half measures.
At some time in the early evening, however, the Tsar received a second telegram from the Kaiser, sent at 6:30 pm, stating that “military measures [i.e. mobilization] on the part of Russia would be looked upon by Austria as a calamity we both wish to avoid.” Immediately upon receipt of this telegram, the Tsar cancelled general mobilization in favor of partial mobilization, hoping the gesture would be enough to appease the Austrian-German sensibilities.
While his advisors seemed fully aware of the implications of mobilization (war), it seems the Tsar believed (or at least hoped) he could mobilize but avoid war with Germany.