A discard can only ever be from the hand. Putting a card into the graveyard from any other zone is not a discard.
Mind, that it doesn't matter where the card actualy goes, the graveyard is just the default. Due to replacement effects, cards can be discarded into other zones as well, like exile. what matters is the action word "discard" for a card to have been discarded.
To answer the other part of your question, the ability happens at the beginning of your upkeep, exactly as the card says. The upkeep step is the second step of your turn, immediately after your untap step when you untap all of your permanents, and immediately before your draw step when you draw your card for the turn.
A few rules you might want to read: 500.1. A turn consists of five phases, in this order: beginning, precombat main, combat, postcombat main, and ending. (…)
501.1. The beginning phase consists of three steps, in this order: untap, upkeep, and draw.
701.8a To discard a card, move it from its owner’s hand to that player’s graveyard.
Mind, that it doesn't matter where the card actualy goes, the graveyard is just the default. Due to replacement effects, cards can be discarded into other zones as well, like exile. what matters is the action word "discard" for a card to have been discarded.
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500.1. A turn consists of five phases, in this order: beginning, precombat main, combat, postcombat main, and ending. (…)
501.1. The beginning phase consists of three steps, in this order: untap, upkeep, and draw.
701.8a To discard a card, move it from its owner’s hand to that player’s graveyard.
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules