The magicians and/or dragons would link their minds before sharing energy. There weren't any visible effects.
Sharing energy was a very useful tactic for Dragon Riders, especially human Dragon Riders. Because dragons had more physical strength and energy than humans or elves, they could easily withstand the loss. Divided, the energy between them effectively doubled what a spellcaster was capable of, making them much more powerful.
Role in the booksEdit
Eragon and his dragon, Saphira, would join minds whenever one of them was in danger, so they would be more powerful then they were alone. Some situations where this happened include healing Brom, confronting the Twins, thwarting Murtagh's scrying spell and trying to break Murtagh's restraining spells.