Instructions
Install PunkBuster on your server. The program's website offers a full range of specifications and installation instructions, as each process is different for the game you are installing the software onto. PunkBuster is dedicated to detecting a plethora of hacks, including Aimbot. Any players detected to be using Aimbot will automatically be kicked out and permanently banned from the server they are playing in.
Enter spectator mode, if available, and examine if a player is moving slowly, if at all, when firing. One of the primary cues of someone using Aimbot is when the player moves slowly but suddenly turns rapidly and begins firing. A player who is not using hacks will typically move around, even when in a fire fight, to avoid the aim of other players.
Ask the player for a screenshot. If you're in a tournament setting, the player is expected to oblige with this request, allowing you to see his screen as he does. If he is using Aimbot, an icon of the program will sometimes be displayed at one of the corners of the screen.
Study what an Aimbot looks like. It is not suggested that you download one and use it yourself, but there are pictures of Aimbots available online at sites that offer Aimbot programs (see Resources). You can see what players who use the cheat see when using the hack.