The official policy of the Qing governmnt was one of "neutrality" in a conflict on their own soil, but this was not a policy of their own choosing. Qing officials, most notably General Yuan Shikai, attempted to side with the Japanese during the war but were rebuffed by the Japanese government. Nevertheless, the Qing did support guerillas who had been fighting the Russians for years during the conflict.
In 1895, Kaiser Wilhelm of Germany, due to a desire to ingratiate himself with Tsar Nicholas and due to his own racial convictions, organized a coalition to force Japan to return Lushun (Port Arthur) to China. That same year, Russia pressured the Qing to give the Port to them, and started construction of the South Manchuria railway to connect it to Siberia. Almost immediately after the Russians arrived, the locals started shooting at them.
Known as Honghuzi, guerillas fired on the Russians despite the small size of their initial deployment out of resentment for prior Russian activities. In 1858, Russia forced Qing to sign the Treaty of Aigun, handing over half of Manchuria (including modern day Vladivostok). Subsequently, Russian troops massacred the Manchu villagers there. The Qing government in 1860 opened Manchuria to Han Chinese settlement (previously it operated as a Manchu hunting estate). The government told settlers to move not only for better farmland, but to defend the country against the Russians.
As a result of the events of 1858-1860, the Russians had acquired a uniquely bad reputation among Chinese, and Manchuria was settled by an especially suspicious and vigilant population. The Russians soon proved that the Manchurians were right to be suspicious - as early as 1895, Russian troops commit indignities against the civilian population.
The Honghuzi were closely related to the later Boxer movement, and this movement would bring yet more misfortune on Manchuria. In 1900, the Boxers laid siege to the Foreign Legation in Beijing, and many imperial powers used this as an excuse to intervene. Unlike the other seven members of the Eight Nation Alliance, who intervened to free the legation, the Russians deployed an absurdly large force of 200,000 to invade Manchuria, attacking Qing troops and Honghuzi alike in the name of "defeating Boxerism". This intervention was extremely brutal, and potentially hundreds of thousands of Chinese were killed and displaced. It had the additional effect of essentially destroying Qing rule over Manchuria, and in the subsequent months, Qing administrators were forced to take orders from the Russians and abide by Russian regulations on trade, tariffs, commerce, and business.
The Boxer Rebellion had one other effect, and that was to effectively destroy the court's authority in most of China. Qing rule had already become decentralized as a result of the court's efforts to suppress the earlier Taiping and Nian rebellions. This suppression effort involved the devolution of authority to local gentries like Zeng Guofan, who raised private armies to crush the rebels. In 1900, the Dowager Empress declared war on the foreigners, leading numerous local strongmen like Li Hongzhang to break away from central authority and pursue their own policy - Li in particular led a pseudo-secessionist coalition known as the Mutual Protection for Southeast China.
In 1904, the outbreak of the Russo-Japanese War presented a fresh opportunity for Qing to recover Manchuria. The Qing government favored Japan due to its better reputation at the time. Wanting to be seen by the West as "civilized" during the Boxer Rebellion, the Japanese army adopoted strict disciplinary standards in regards to atrocities and acquired "regimental wives" (prostitutes) to limit rapes. This made them seem humane in contrast to the other members of the Eight Nation Alliance, who massacred and raped at will, though one must note that the bar was extremely low.
As a result of these sentiments and his own self interest, Yuan Shikai, the most powerful military commander in China at the time, attempted to aid the Japanese army. For a number of reasons, the Japanese rebuffed him. First, the presence of Chinese troops would diminish the prestige and honor of the Japanese army's victories. Confident they could win by themselves, the army did not want to share their victory. Second, the cabinet knew that Qing presence on the Japanese side would mean the Qing would be at the negotiating table. Unbeknownst to the Chinese, the Japanese did not want merely to expel the Russians from Manchuria, but to inherit their position as the province's controller. This ran against the current of their propaganda - to gain the goodwill of the British and Americans, the Japanese condemned Russia's attempts to turn Manchuria into a territorial colony and limit the market access of other countries. In practice, they wanted to do the same thing, just with fewer massacres and PR failures. Third, Yuan's offer was almost certainly motivated by a desire to become "Japan's man in Manchuria" after the war. Problematically, Japan had already chosen a man - Honghuzi commander Zhang Zuolin. The Japanese army had hired Zhang's band, aided them in eliminating rival bands, and, after the war, helped them gain official recognition as a unit in the Qing army.
Ultimately, the Qing were in an awkward position of "forced neutrality" during the war. Though some of their gifts of food and supplies to the Japanese were accepted, their offers to join the war were not. By the end of the Boxer Rebellion, the Russians had essentially evicted Qing authority and military power from Manchuria, and their ability to influence the course of the war was limited in any case.
Sources:
Bonavia, David. China's Warlords.
Qin, Chen. The Northern Warlords Era.
Nagayama, Yasuo. The Russo-Japanese War.
Yokote, Shinji. History of the Russo-Japanese War, The First Great Power War in the 20th Century.
Sato, Kimihiko. The Origin of the Boxer Movement.