The infantry in the Second Boer War fought mostly with rifles. The British Army used standard issue rifles of the time, which were the Lee-Metford Rifle and the Lee-Enfield Rifle. The Boers, largely supplied by Germany, used Mauser rifles and Danish Krag-Jorgenson rifles. The British rifles had 8 round magazines and the Mausers were accurate to about 2000 meters.
This war also saw the use of some automatic light artillery. The Boers had a weapon known as the Pom-Pom which could rapidly fire 1 pound exploding shells. The British used a variety of artillery pieces, including 12 and 15 pound field artillery that had a range of about 5,000 yards.
Of course, many other weapons were used to some extent in this war. Please follow this link for much more on the subject.