you must have reincarnated from an ancestor (meaning you must have died and inherited stats from your last characters runestone). once you have an ancestor you need to build your ancestor shrine. you cannot pray at any other shrine except the one you made. if your ancestor shrine is destroyed for whatever reason any numen points you have gained and havent used will be lost by a ceratin amount.
now onto actual praying. when you open the character window there is a tab called worship, and it shows you 3 items. the most left item is the item your ancestor wants. if you hold this item in your hand and right click the altar it will be sacrificed and you can either get numen points or nothing depending on your tradition/belief slider. the middle item and right item are two items you can sacrifice to change what items your ancestor wants if you cant find the left one. you are not awarded any numen for this. you can also click the forfeit button and it will sacrifice half your numen points to change the items.
tl;dr
http://havenandhearth.wikia.com/wiki/Ancestral_Worship