It's fairly simple...you give them stuff. Old weapons, armor, items, sweaty gym socks, your ********** whatever. However, you can only give them stuff they will value (the socks might get a point or two, but your ********* are questionable). You accumulate points from donating said items. A section should be on the top left corner of the tribute window with a list of ablities you can use, useable ones will be highlighted, along with a point cost. I gave a bunch of crap (including some no drop weapons) and got an A$$ of points. the abilities run on a timer. mine went for 10 hours, not sure for everyone or all abilites.
Some are pretty cool...like extra damage, resists, focus affects. Others i'm not too sure about. then again, that's prolly why they gave so many.