The names and their meanings
A common list of twenty-one, the one used in the leaf puja, is: Sumukha, the one with a pleasing face; Ganadhipa, lord of the ganas; Umaputra, son of Uma; Gajanana, the elephant-faced; Harasunu, son of Hara (Shiva); Lambodara, the big-bellied; Guhagraja, elder brother of Guha (Kartikeya); Gajakarna, with an elephant's ears; Ekadanta, with one tusk; Vikata, the formidable; Bhinnadanta, with the broken tusk; Vatu, the young student; Sarveshvara, lord of all; Phalachandra, with the Moon on his brow; Heramba, protector of the weak; Shurpakarna, with ears like winnowing fans; Suragraja, foremost of the gods; Ibhavaktra, the elephant-mouthed; Vinayaka, the supreme leader; Suravandya, worshipped by the gods; and Kapila, the tawny one.
Another well-known set, the twelve names recited daily, begins "Sumukhashchaikadantashcha Kapilo Gajakarnakah", and promises that one who recites them at the start of any work, journey or study meets no obstacle.
How the puja is done
After the main worship, take 42 blades of durva, or 21 pairs, and offer a pair at Ganesha's feet or on his head with each name, saying "Om Sumukhaya namah", "Om Ganadhipaya namah" and so on. At the end offer the last blade with all the names together. The same names are used for the 21 leaves and the 21 modaks. Recite with attention to the meaning; each name is a way of remembering a different side of the god.