After you've grown a few inches or so of "new growth" (natural hair that has grown in weeks after you've relaxed your hair), doing the big chop alleviates the stress of having two different textures in your hair. Maintaining two different textures in your hair for a long time can be damaging, because the relaxed, straight hair weighs down your natural curls and causes breakage. Therefore, the sooner you cut the straight ends off, the quicker your natural hair will start to flourish.
Wet your hair with water from a spray bottle. You don't have to saturate your hair, but make sure that it's very damp. Wetting it like this causes your natural hair to curl up more tightly, which makes it much easier to distinguish the relaxed part of your hair from the natural curl.
Look at a section of your hair, and identify where your natural hair ends and where the relaxed hair begins.
Cut your hair at the point where the natural hair ends and the relaxed hair begins. If you're nervous, cut about 1/2 inch before that point. You can always come back to it and cut more off later. Do this for your entire head of hair.
Section your hair off into four to eight sections, depending on how thick and long it is.
Re-wet your hair, and snip off any straight ends that remain.
Wash your hair thoroughly to remove any loose strands. If you leave them in your hair too long, they will just get tangled up.
If you're not ready to cut off all your relaxed ends, just cut off a few inches at a time. Although cutting your hair in sections isn't necessary, it will make the process much easier. Take your time. You can always go back and cut pieces that you may have missed.
Make sure you're using hair scissors. Any other type of scissors will damage your hair. If you're using a comb to detangle, be gentle and comb slowly from the ends up.