The Constant Combinator broadcasts up to 15 values on any of the channels for whatever networks it is connected to. (You cannot currently specify whether a value should be red or green; if you need different values, use two combinators, one for each color wire.) You can use any item channel or any of the Virtual signal channels.
Note that using two of the 15 slots to broadcast values on the same channel is the same as broadcasting the sum of the two values from one slot.
The Arithmetic Combinator performs arithmetic operations on input values and broadcasts the result to the specified output channel. The input and output channels can be any item channel or any of the virtual signal channels.
Connecting: The Arithmetic Combinator connects to a red or green network on its input side (the terminals are set into the main body and look like spark plugs) and performs an arithmetic calculation which is broadcast into the specified channel on its output side (the output wires appear to stretch out a bit from the body of the device).
Feedback: Note that the input network and the output network are not the same network. Connecting the output network back to the input network will result in a feedback loop. For example, adding 1 to the value for Copper Plates and broadcasting it as Copper Plates is an action that results in an infinite loop if output is connected back to input. The value for Copper Plates will rapidly (but not instantly) shoot upward. This technique can be combined with Decider Combinator logic to make electronic clocks, gates, and other systems; see Combinator Tutorial for advanced techniques.
Each: This combinator can use the 'Each' signal for both input and output, in which case all non-zero input channels will have the combinator's operation performed and broadcast on the output side. Having Each signals for input and output and using a non-changing operation (like adding zero) is equivalent to having a 'one-way' wire; all the information from the input network is copied to the output network, but the reverse is not true.
Multi-network: The Arithmetic Combinator can be joined to both red and green networks on the input side and will sum their inputs.
The Decider Combinator functions much like an Arithmetic Combinator, but is designed to compare values from red and green networks. In terms of Connecting, Feedback, and the Each signal it functions as specified above. In addition, it can handle the Everything and Anything signals, and performs more complex functions than summing when attached to multiple networks. See the Decider Combinator page for more details on how to use this.