The truth is that how the Russian people felt about anything was completely irrelevant, the Tsar was an absolute autocrat. Although the Duma was more or less a parliament of sorts, they had no actual power over any decision the ruler made. Many Russians supported the war as an act of solidarity with fellow Slavs in the Balkans, but these would have been military officers and politicians. The people of Russia as a whole had little or no idea of what was going on in the world outside of their locality, the great mass of Russians being uneducated people living in rural areas, for all practical purposes cut off from the rest of the world. Those in the cities were more informed, but largely opposed to the war. People were often supportive of war against Austria-Hungary, but they feared war with Germany (with good reason).
The military command structure supported the war, for personal and professional reasons, although Grand Duke Nicholas (the tsar's brother, who was made commander-in-chief of the army) thought it would be a disaster for the country and likely lead to revolution. It was said that he cried upon being informed of his appointment.
The Russian war plan was foolish in the extreme. To relieve pressure on the French the Russians intended to invade East Prussia before their own mobilization was complete, thereby hoping to throw the German war machine out of balance. Operations against Austria went well, since the Russians had (through their effective use of spies) the complete Austrian war plans years in advance. Against Germany, the Russians foundered. They sent two Armies into Prussia, one south and one north of the Masurian Lakes. These two (the First and Second Armies) were to coordinate somehow, with no possible means of communication, and with both commanders hating one another. Under a retired Prussian general recalled to duty (Paul von Benekendorff und Hindeburg) and a logistical wizard named Hoffman the Germans moved their forces by lateral railways and crushed one Russian army at Gumbinnen and the other at Tannenberg in a matter of days. From this point on the Russians were fighting a losing war against Germany, which eventually cost the Tsar his throne in spring, 1917, and then the Kerensky government to fall to the Bolsheviks later in the year.