In order to curl your naturally curly hair make sure it is straight. separate sections, it might be easier to curl in vertical sections, at least for the first time, act like its all one layer until you get the hang of it. depending on how tight you want the curl pick your curling iron. i would suggest a one inch, because i haven't had any results with one smaller, it didn't seem to work. place the clamp on the ends on your hair, and take care to separate any hair that isn't as long as the end you are curling or slide the iron up to clamp shorter hairs also.
when you start the curl, curl in the natural direction of the iron, don't wrap the hair so that it is doubled over the clamp on the first turn make a smooth circle or you will have an odd direction at the can wrap your hair on top of it self as you wind all the way up, for a more polished look, only curl as far up as your ears.hold the iron vertical, position it as you wrap the hair. and hold for 20-30 seconds, depending on the size of the section, small sections only take 5-15 seconds. larger ones can take a maximum of 35-40 just be careful not to over do it.
i recommend spraying each curl with hairspray while its hot. and covering your hair in hairspray before you start. also you don't need an expensive iron, just one that's not too old or small. i bought a mini on ebay for 5 dollars and it works like a dream. getting the back of your head may seem a bit more difficult try to pull the hair to the side so you can see the ends, and be careful about the position, making sure you wrap and hold vertically. you will get the hang of it.
you should get pretty spirals with a tiny amount of practice. maybe 10 mins. i know it seems odd to curl your naturally curly hair, but everyone dreams of a looser curl pattern once in a while, and you will find it easy to achieve a model look in no time. curling is much faster the straightening. and if yo mess a curl up, don't fret, you just have to re-straighten it to get a fresh canvas. practice on your bangs first hope i helped!