This is biggest change to the TFT rules. Players may become clerics by putting points into a new attribute called "Piety" (PY). People who want to do serious kick butt stuff with clerics will eventually want to put 5 or more attributes into PY. Piety has a superscript called "Devotion" (dPY) which is added to PY when you are using Undead Effects to fight or control undead.. If you have a 3 PY you may learn a maximum of 3 holy rites. (Sometimes gods will give extra rites to people, so if a god wishes, you might have a PY of 3, but 5 rites.) To be explicit, rites to not use up your memory, so clerics are free to learn normal spells and multi-class as fighters, rogues, etc.
There is NO list of rites for anyone or any god. Each rite is a 1 on 1 miracle that the god has given to that particular worshipper, and is unique. Some gods are not that creative and tend to give their clerics similar lists of rites (tho individual variation is always possible). Most gods seem to have a favourite rite or two that many of their clerics get. But, fundamentally, the rites that the PC gets are unique. This makes fighting clerics a bit nerve-racking. You often have NO idea what they can do.
When you increase your PY, existing rites may become more powerful. This usually requires some time spent praying in a holy place. At that time, new rites for any additional PY that you have earned are gained. Players may pray for certain types of rites. (e.g. "Please Thor, give me a kick ass hammer that shoots huge lightning bolts!", but what they actually get may be a bit different. "Dear Thor, I would like to thank you for the Summon Bar Wench rite. Your ways are mysterious my Lord..." .)
One difference between PY and regular attributes is that the maximum PY is very low. The maximum PY is 1 for all characters. If you take Acolyte it is raised to 2, if you take Priest it is raised to 3 and if you take Theologian it is raised to 4. By doing acts that your god approves of (e.g. finding more worshippers, upholding your god's moral code), the maximum PY can be raised. If you piss off your god, your max PY can be lowered. Thus max PY is in a real sense, how good an odour you are with your god. Devotion can be raised by the god, especially if you are fighting undeath. This often is done as a miracle which costs no experience points, and at the time it is raised a new rite is given to the cleric.
This campaign has many 'small gods' who have limited areas of power. The power of gods seem to be somewhat based on their worshippers, so if you worship a god and move far from his place of power, he may lose some potency, but fundamentally he follows you and your heart. It is known that the more worshippers a god has, the more powerful the god becomes. (And if you can get a bunch of worshippers in your new lands, maybe he will start paying more attention to this area!)
Some religions allow their priests to fight undead. These require rolls verses PY. For example to 'turn' a zombie might require a roll of 3vs (PY + dPY + 6) (because zombies are easy) where as to turn a vampire might require a 4vs (PY + dPY - 2) (because vampires are very hard). The exact rules vary from religion to religion.
Finally, there exist undead diseases and parasites called 'ague'. Cleansing works by killing things that are not you. However, ague are already dead, so the Cleansing spell has no effect on them. Vampirism and Lycanthropy are examples of ague and no longer are affected by the Cleansing spell.