The 'random start' button restarts the simulation with a random initial configuration, but does not change any other settings.
The 'width' and 'height' parameters control the number of pixels wide and the number of pixels high the display is. The width is equivalent to the size of the world and the height is equivalent to the number of generations performed (or rather 1 more, because the initial configuration is generated randomly). The total number of pixels in the display is equal to the product of the width and the height, so be careful when setting it to high values (for instance, 20000X20000 would take over a gigabyte of memory).
The 'state count' parameter determines the number of possible cell states. Each state is represented by a color of pixel. The colors for the states can be set manually below the input for the state count. Note the number of possible neighborhoods is the cube of the state count, so be careful when setting it to high values (anything above about 10) as that can cause the browser to crash or suck up huge amounts of memory.
The 'random rule' button generates a random rule with the current number of states. The 'random rule (isotropic)' button does the same, but ensures that the rule is isotropic (that is, it is its own left-to-right mirror image). The 'order' parameter roughly determines the amount of order present in the rule. Completely random rules with higher numbers of states tend to look too chaotic to be interesting, so increasing this parameter can help to generate rules that produce more interesting patterns even with relatively high numbers of states. Below these settings, the outcomes for individual neighborhoods can be specified manually.