How to power a nickel chromium wire to produce heat without burning the power adpapter
A typical two-slice toaster uses around 1kW.  That toasts about 4 x 5" x 4 = 100 square inches of surface. 

You have no more than 24W. If we can do as well at lower powers, you would be able to toast about 2.4 square inches of surface or about two 1.1" square (27mm square) pieces. Not even the size of a piece of melba toast (and that comes pre-toasted). Maybe you can toast one side at a time, but still rather small. 

Anyway, to calculate the resistance you decide whether to connect the (presumably) two sides in series or in parallel, and calculate the resistance from Ohm's law. 

For example, to use the 24V you might connect them in series. You need 24 ohms to get 1A, so each one should be 12 ohms. Find a size of nichrome wire that will allow a decent watt-density (you want enough surface area that the wire will not burn up and will cover your desired surface area reasonably evenly). Here is a link that will help with estimating the desired wire gauge etc. 

But it's not really much fun to make something that doesn't work, so I think you should re-think the power source unless you're making toast for your gerbils' breakfast.