Damage

Whenever the Runner takes damage, s/he must trash one card at random from grip for each point of damage suffered. There are three types of damage: Meat Damage, Net Damage, and Brain Damage.

Page 20, Column 2, Paragraph(s) 3, Core Rule Book
Many cards and ice subroutines inflict damage on the Runner.

Brain damage has a lasting effect on the Runner, while meat and net damage are only different by the cards that inflict and prevent them.

Page 20, Column 2, Paragraph(s) 7, Core Rule Book
Note: The only differences between net and meat damage are the cards that inflict and prevent them.

If the Runner takes more than one damage at once, then s/he randomly trashes one card at a time for each point of damage, placing them in the heap in the order randomly chosen.

Page 20, Column 2, Paragraph(s) 8, Core Rule Book
When the Runner trashes multiple cards for damage, the cards are placed in his heap in the order they were randomly trashed.

Rulings

If more than one point of damage is suffered as a result of a single ability (e.g. Scorched Earth, Snare!), all points of damage are considered to be suffered simultaneously. Cards are trashed one at a time to maintain the order of the heap, but the damage is still considered to be suffered all at once. Thus, paid abilities from cards such as Plascrete Carapace and Feedback Filter cannot be activated partway through the trashing process and must be activated before any cards are trashed, and cards that trigger off of receiving damage (such as I've Had Worse) resolve their effects after all damage has finished being dealt from that single ability. For more information, see the I've Had Worse Timing Clarification.

Damage can be either "done" to the Runner or "suffered"/"taken" by the Runner. Damage that is dealt to the Runner results in the Runner suffering damage, but not all damage suffered by the Runner is dealt. For more information, see the Damage Terminology Ruling.

See Also

The Runner can lose the game if s/he takes too much damage. See Flatline.