It's basically random. When you hatch an egg, it has a chance to come out any of the eight natural colors. It's just that natural itself is the most common.

For the dye colors, you just have to buy a dye kit and use it on a pet. They can be found in the Black Market or user shops - although, they are pretty expensive.

You get coloured creatu by hatching them, 'beaning' them, dyeing them or buying them from other people. =3

Hatchable colours are: Natural, Cream, Sepia, Black, Ginger, Silver, Blonde and Albino. Natural is the most common colour and albino is the rarest. People can go through long 'nattie streaks' where they may only hatch natural coloured creatu for days or weeks on end - this is more likely to happen if you are a merchant.

'Beaning' means to use a natural coloured jelly bean on your pet. This is a credit shop item which randomly changes the colour of your pet to any colour except natural.

You can dye your pets different colours too by buying Dye Kits from the Black Market or from user shops. Dye colours available are: Amber, Azure, Indigo, Gold & Silver, Lemon, Lime, Magenta, Orchid and Rose.

But please note not all creatu are available in the colours I've mentioned :P If you go to your Hatchery and click on Creatu List, you'll be able to see all the creatu on rescreatu and what colours they come in.

By 'special' rescreatu pets, I'm going to guess you mean things like Omni, Iluvu, Wyrae.. etc.

Iluvu, Easero, Jaaku, Ebilia and Uilus (and possibly Narwi too one day)  are seasonal or holiday creatu which can only be found around the time of their respective holidays. Iluvu around Valentine's Day, Ebilia around Halloween etc. The eggs cannot be found outside their holiday but they and the creatu themselves can be bought from other users.

Aerix, Cyid, Ezahni, Haberisar, Kioka, Liyure, Omni, Shaefu and Wyrae are Credit Shop creatu. You can buy the eggs from the credit shop with credits which have been purchased with real money or with tu. Or you can buy the eggs or creatu from other users. Credit Shop pets cycle in and out of the shop; last month Ezahni were in, right now it's Cyid. Some of the pets have retired and won't be seen in there again so you'll have to buy those from other users. Wyrae are a bit special in that you have to buy a Random Morphing Potion (RMP) from the credit shop in order to get one. An RMP can randomly change your creatu into any non-cs pet or a wyrae. You may get a wyrae on your 1st attempt or on your 30th attempt - it is completely random. 

Ivik and RSTU001 can only be obtained by completeing Kir's Quest (see Games > Quest) or by buying them from other users. :P

Sorry that was a bit long and you probably already knew some of it ^^; But I hope you find it helpful.