Programs are what machines, such as mechs, use to carry out certain activities that they otherwise wouldn't be able to do. Programs use one of the four abilities of a machine (Hull, Engines, Reactor, Systems). Each program description will explain under which circumstances they can be used and its effect.
Just as machines rely on their Reactor score to arm themselves with Artillery, programs rely on the machine's Systems score. To determine how many programs your machine can have installed, times your Systems score by 2. If, for example, you have Systems score of 3, you can load 6 programs. As explained in the Mechs section of this manual, a machine's ability score determines the ability challenge rating (CR) and the ability points. A Systems score of 4 equals 2 System ability points and 8 program slots. See that part of the manual to understand how machine points are allocated.
Each program you load will have its own requirements as well. Some programs will require you to have a certain number of points in each ability in order to use it. If you have 4 programs loaded, and one of the programs is Short Circuit, for example, it will require you to have at least 1 Reactor point (RP) as well. If you just wanted Short Circuit, and no other program, you would need a Systems score of 1 and a Reactor score of 2, that way you will have at least 1 slot for the program and 1 Reactor point (RP). Study the programs carefully so you know how to distribute your machine's ability points.
When a machine must make an ability check, it is to roll 1D20 and add the machine's ability score to the roll to see if they can overcome the engaging machine's CR.