Hey there!
Different effects are obtained in different ways. Just bear in mind that not all species can get all effects yet. You can use the pet directory or creatu colors pages to check! Pets have to be adult for effects to show, with the exception of the derp effect, which is available for all stages.
Frostlight: use a frost light icicle on your pet, or take your pet to the ice tunnels during the winter events
Stardust: use a stardust urn on the pet (different coloured urn depending on what planet the pet is from). Urns are made by 'using' a stardust urn and putting stardust in it, except for gold urns which are bought from the cash shop.
Cosmic: use a cosmic salve on the pet (these are purchased in the cash shop)
Undead: resurrect an adult pet from the graveyard with a curse of the undead (obtained from Halloween event)
Derp: hatch a pet during April Fool's event
Ageless: use ageless extract on your pet - 1 for teen and 2 for baby
Elemental: visit the shrine and build up your reputation until you get a blessing. Pets can only be blessed at the shrine on the planet they come from and you can only access the shrine of the planet you are currently living on.
For the shrines, your reputation is best earned by handing in pets from whatever planet you're on. The rarer the pet, the more rep you will get, so better colours and seasonals will give you more points. You can also hand in eggs and items and they all have different values so it's best just to try it out and see what sorts of items give the best points.
You can't directly exchange tu for Cash Points but you can buy them from other users, so you just have to find someone selling them. At the moment I think they go for around 1mil per cash point.
Hope that helps! Feel free to reply or rmail me if you have any more questions.