I am running 4 new recessed lights with a 12/3 wire to a new dimmer switch. I just want to make sure this will work on a ## amp fuse with an existing light fixture on the same line. I am not too familiar with running new lines and if you can give me any tips that would be helpful

Why not just tell us what you want to do and let us tell you how to do it. Why 12/3 cable. 12/3 wire or cable is 12 gauge wire with three conductors and a ground. Meaning that 12/3 cable has 4 wires.

What size wire was used in the existing circuit? What size is the breaker for the circuit, 15 amp or 20 amp?
Is existing light the only thing that is on the circuit now.

For what ever reason your fuse ampacity shows up as ##. You can use 12AWG in a 15 0r 20. Your limiting factor here will be the dimmer as it is probably rated for 600Watts. It will handle more but overheat. From what I can read, you will have 5 lights on a 12AWG. Should be no problem. As far a wiring them, run neutral white to the first light, black through the dimmer to the first light and then black and white to the other lights. You will need dimmable CFL's if you are planning to use this type of luminaire. You will need a 3 way dimmer if the current wiring is 3 way. If you are not experienced with running wires, get some help or use an electrician. Even 120V can kill you.