First you have to remove the chain. Normally, one tends to also replace it when replacing the chainrings. If so, you can simply use a strong pair of bolt cutters to open it. Otherwise, simply use your chain tool. Before removing the chain, make sure it sits on the smallest ring in the front and the smallest cog in the back. This way it experiences the least amount of tension. Most new derailleurs also have a lock function to decrease chain tension and make removal easier. Either way, be careful when the chain snaps open.