In the modern era, camel cavalry, much like horse cavalry, was increasingly used as a kind of mounted infantry by Western powers. Troopers rode on camels and horses until they made contact with the enemy and then dismounted and fought on foot.
In fact, there are cases where horse cavalry were converted to camel cavalry and infantry were mounted on camels, then formed into one unit. During the Gordon Relief Expedition of 1884-1885 in Egypt and the Sudan, the British army created a temporary "Camel Corps." In an (ultimately unsuccessful) effort to rescue "Chinese" Gordon's besieged forces in Khartoum, British commander Sir Garnet Wolseley took some of his troops and put them on camels, hoping the better cross-desert mobility of his "Desert Column" would help them get to Gordon. Spoiler: Khartoum fell well before the sluggish British advance across the desert and down the Nile could get there
Like I mentioned earlier, the Camel Corps pulled in troops from a range of postings. Given their dramatic mission, it was something of a high-status posting. One of the Camel Corps' regiments (the Heavy Reigment pulled from the socially-elite Household Cavalry and the less-prominent, but still flashy regiments of "heavy" cavalry like dragoons and lancers. The Light Regiment took troops from the "light" cavalry hussar units. The Guards Regiment of the Camel Corps tapped into the elite troops of the Household Brigade, taking in the men of the Grenadier, Coldstream and Scots Guards. The Mounted Infantry Regiment simply took in men from the infantry regiments already in Egypt.
When it came time to fight, the Camel Corps would dismount and fight as infantry. In this case, very little thought was given to them fighting while mounted.
Still, there were some differences. Horses, even well-trained ones can be skittish and easily spooked. When fighting dismounted, one in four men had to be sent to the rear as a horse holder. He had his hands literally quite full with four horses and couldn't realistically handle any more. This obviously diminished the firepower of a dismounted cavalry unit somewhat. It's also why many basic cavalry units are divisible by 4. For example, the pre-WWII U.S. Army cavalry squad has eight troopers: two men for horse-holding, six men who can fire.
During WWI, the British formed the Imperial Camel Corps, a camel-mounted infantry force of Australians, New Zealanders, and British troopers. Like most horse cavalry units, they used the "three shooting-one holding" formation when fighting dismounted, so their most basic unit was a four man "group."
However, during their service in the Middle East, they learned that camels were a bit more level-headed than horses. This quirk of camel behavior let them modify their tactics a bit.
At first, when in battle one trooper from this group was expected to stay behind and guard the four camels while the other three went into action. This was the drill used in the horse-mounted infantry units then in Egypt.
However in practice the troopers found the camels were a lot easier to control than horses once they were barraked (made to kneel down). They were also much less prone to panicking when exposed to enemy artillery and small-arms fire. Therefore it soon became normal procedure for one man to look after 12 or even 16 camels once they were barraked.
During the Gordon Relief Expedition in 1884-1885, the Camel Corps went even further. During battles, soldiers dismounted and tightly hobbled their camels and left a few men to guard them. This prevented the camels from running away and eliminated the need for a large number of camel-holders. The soldiers could then move out to fight in a line. Or they could form a hollow square, with the infantry at the center of the formation.
However, there were also some drawbacks to camels, particularly when in came to speed and easy of mounting/dismounting. This October 1884 memo issued by then-Brigadier Redvers Buller illustrates these problems quite well.
The soldiers of the Camel Regiments will fight only on foot. They are mounted on camels only to enable them to make long marches. The camel is a good traveller; but he is a slow mover.
He cannot be managed as easily as a horse, and he cannot be mounted, or dismounted From, with great rapidity. The men of the Camel Corps must therefore trust dolely to themselves and their weapons when once they have dismounted, This cannot be too strongly impressed upon the men. If we have to fight in the Sudan, we must expect to meet an enemy far outnumbering us, and who may at first charge recklessly home, apparently regardless of the intense fire we bring to bear upon him.
The attack formation far infantry of our Drill Book is not intended to be employed against an enemy like the Arabs of the Sudan, It is designed to enable infantry to advance with the least possible lost over ground swept by a heavy fire from guns and rifles of an enemy as well armed and disciplined as ourselves, against whom an advance in close order would be impossible. In acting against Arabs who are Indifferently armed and bad shots, the open formation of the Drill Book is not necessary."
Because of the respective limitations of camels and horses, many armies operating in the desert used a combination of the two. At the Battle of Abu Klea in 1885, for example, the Camel Corps dismounted to fight as infantry in a large square.
Meanwhile, the 19th Hussars fought on horseback. The hussars acted as piquets and scouted ahead of the slower-moving main body of camels, infantry and artillery. Interestingly enough, future WWI BEF commander (then just a Major) John French was with the Hussars when they first spotted the Mahdist forces they'd fight at Abu Klea. During the battle itself, the cavalry remained outside the square, charging a force of Madhists to take the vital wells at Abu Klea.
Sources: The Imperial Camel Corps: Cameliers and Camels at War https://nzhistory.govt.nz/war/camel-corps/camels-and-cameliers
History of the Sudan Campaign, Volume I and Volume II by Sir Henry Edward Colville.