To start prayer, you simple need to bury them, or more preferrably use them on altar for more xp.
Use commando ::home or ctrl + h to use the altar right next to the bank.
A very handy tool to train prayer is to use the bonecrusher.
It crushes the bones dropped from monsters and grants you prayer experience.
This tool can be purchased from slayer shop for 25 points.
Keep in mind that using the bonecrusher doesn't count towards achievements.
Bones
Bury xp - 125
Altar xp - 350
Bonecrusher xp - 250
Drop - Most monsters
Bat bones
Bury xp - 306
Altar xp --
Bonecrusher xp --
Drop - Bats
Big bones
Bury xp - 250
Altar xp - 350
Bonecrusher xp - 500
Drop - Alot of monsters, primarily hill giants and moss giants
Babydragon bones
Bury xp - 750
Altar xp - 750
Bonecrusher xp -875
Drop - Babydragons
Ourg bones
Bury xp - 825
Altar xp - 1150
Bonecrusher xp - 1875
Drop - General Graardor
Wyvern bones
Bury xp - 1000
Altar xp - 1250
Bonecrusher xp - 1000
Drop - Skeletal wyvern
Bury xp - 1250
Altar xp - 1800
Bonecrusher xp - 1250
Drop - All dragons
Magma bones
Bury xp - 1275
Altar xp - 2150
Bonecrusher xp - 1375
Drop - Magma beasts, Magma elemental
Frost dragon bones
Bury xp - 1750
Altar xp - 3750
Bonecrusher xp - 2125
Drop - Frost dragons, Celestial dragons
Ebon dragon bones
Bury xp - 2000
Altar xp - 4845
Bonecrusher xp - 2250
Drop - Ebonchill dragons
Special
Firey ashes
Bury xp --
Altar xp - 500
Drop - Fireland Monster
Chance to recieve goodies and rares while praying at altar.
Achievements manager
I would recommend checking the achievements manager before completing tasks as some prayer training methods are rewarded.
PS: No experience boost was added.