Prayer differs from other skills in the way it is trained. You do not unlock any higher xp rates as you progress, rather, you need to advance other skills to train prayer more effectively. Remember that it's highly inefficient to train prayer by itself, and it's best done as bonus xp while training other skills.
If you wish to know more about imbuing, burning and incinerating bones, refer to the incinerator page.
This guide will focus mostly on different ways and methods of quickly obtaining bones and using them for yourself. if you decide to sell them instead, you might gain sizeable amounts of money.
Pre-obtaining bones[]
Usually obtaining bones is done fastest while killing large amounts of easy-to-kill enemies, same as thieving leveling. For example you can farm Al-Kharid warriors (refer to the thieving guide) and bank their bones, since the bank is next door. Same story with thieving wizards south of Falador.
When you have your bones banked, next step is to run them from a bank to an altar, imbue them, and run back to the bank to get a new set of bones. The best spot for this at the moment is in Lletya, though Varrock and it's red tent work well too.
If your firemaking level is low but you still want to achieve higher rates of xp, you could also use the Incinerator in the Mausoleum. Though as it is quite far away from it's nearest bank, this isn't generally recommended.
Training prayer in Taverley dungeon[]
Reqs: High firemaking
A very interesting and practical way of training prayer is through slayer in taverley dungeon. All you need to do is take 1-2 (depends on your clicking speed) of the highest level logs you can burn along with you for every slayer trip.
As your food/prayer pot supplies dwindle, you'll be filling your inventory with bones (taverley dungeon contains all types of bones). Once your inventory is full, you can go to the altar in the last room of taverley dungeon, imbue your bones, and burn them in your own fire on the spot, then you go back to bank to refill your supplies and repeat. with 90FM, this method provides x3.8xp multiplier for Prayer.
If you're using range/mage and not using up any supplies, you can take 6-7 logs and refill only every 6 or so inventories of bones.
Training prayer on Hill Giants[]
Reqs: Ability to kill Hill Giants in 2-3 hits, 50 cooking.
Another very effective method training prayer is in Edgeville Dungeon. There you can kill Hill Giants, which give Enormous Bones. Then, after getting a full inventory of Enormous Bones, you may climb up the ladder and exit at the top with the use of a Brass Key, and bank the bones in the Cooking Guild. After you are pleased with the amount of Enormous Bones you've gathered, you can go to the previously mentioned imbuing spots, and imbue your bones. And with all your imbued bones you can wait for DXP, and bury them in the highest level fire you can for maximum exp.
With 90FM and two-shotting with a bow, you can get roughly 100k/xp prayer per hour, accounting for the time spent banking and imbuing.