Cynical and aloof, Archer doesn't seem to care about the grail war from the perspective of actually obtaiing the grail. He fights, but only as he is expected to do so. He has a quirky relatioship with his master Rin. The two argue a lot over trivial things, but are focused and well coordinated when it comes to the grail war.
From the very beginning Archer and Shiro don't get along. At first Shiro thinks this is only a bad first impression, but the situation between them never improves. Even so, Archer occasionally gives Shiro helpful advice. This often forshadows a critical event Shiro must overcome with an ability or understanding he doesn't yet possess.
Although summoned as the class archer, he prefers to use twin swords Kanshi and Bakuya in melee combat. Another of his trademarks is to shoot weapons of a noble phantasm level from a bow. Archer can summon weapons, and enhance them as well. Simply by looking at them, he is able to analyze their structure and duplicate them through projection. Being in the archer class also gives him keen eyesight.
Archer has various noble phantasms but most of them are fairly weak compared to the other servants. With each servant he battles he acquires knowledge of their weapons. The limitation of this is that he is simply the owner of such a weapon he duplicates, not the true master. His only defensive ability is Rho Aias: a legendary shield that can withstand attacks both great strength and number. This manifests itself in a magical looking flower with seven petals, each with the property of the shield. His main noble phantasm is the ability to twist reality into another dimension called a Reality Marble. There, Archer can call forth weapons instantly whereas in the outside world he actually has to summon them.
Archer is an unusual servant for many reasons. He claims he doesn't remember who he was in his previous life. Although summoned as class archer, he fights with swords and can summon heroic level weapons at will. Servants try to hide their true identity, but for Archer this is easy as nearly everything about his fighting style goes against how servants normally fight. It's later revealed that he was once a magus that wanted to help people, and became a heroic spirit to save them. However as he was summoned into grail war after grail war, he saw nothing but killing and destruction. Time after time he would save some people, but in the end there was always the killing. It never seemed to end. His participation is to minimize casualties rather than obtain the grail itself.[ + ] Show Spoiler:
In Unlimited Blade Works it's revealed that Archer is in fact Shiro: the winner of the fifth grail war. He is the ideal that Shiro wished to become: a strong warrior capable of saving other people. Heroic spirits exist in time separate from our reality. They can come from any point in history; the future, or present.
In a strange story arc, Archer reveals that through all the killing he's done he came to believe that he was naive in his ideals when he was alive. Archer wants nothing more then to end it, and thus had hoped all this time that he would be summoned during this grail war so that he could kill himself before becoming a heroic spirit. This is demoralizing to Shiro. All his ideals are realized, but became twisted once summoned as a heroic spirit.