wheres a good place to start with this project!! i want a timer with an on time of 1 second per minute.
i want it to control a contactor.
The "Blink" and "Blink without-delay" sketches found in Arduinos IDE would work fine.
The first one simply delays all functions until it's time to switch a device on/off but does nothing else.
The second one checks time, acts when it's time and gives you the possibility to, for example, add an LCD-display to see who many seconds are left in the mean time.
Instead of using 1sec on/ 1sec off it's easy to just change the values.
You could quite easily run it on arduino and use its led on pin 13 to check/adjust the program.
To add a contactor or relay, you probably need a bit more hardware as well, those often use more power as an arduino can handle. Without the chance of ruining your Arduino is high.
http://www.arduino.cc/playground/uploads/Main/relays.pdf shows you an example to control a transistor, which... can handle more power and control the relay.
I don't know what... voltages you would like to control or what your experience is, please do keep in mind high voltages can be extremely dangerous. (x1000!)