A long rest lets you get up to half your HD back (used for short rest healing).
All numbers round down.
A 1st level character can never get a HD back (1/2 rounded down)
This is an error. It's minimum 1.
Though you usually get to level 2 with just 1 day of fighting.
Yeah, level 1 - 2 is 300 XP 
AH_Central_Command wrote:
Yep Mike Mearls IIRC answered a tweet about this and stated that it should have been written minimum 1.
It's in the Basic rules now:
Page 67 Basic Rules wrote:
Nice. I was just ruling that they gained half of their HD back... so it took two long rests to get the 1 HD back. Glad they modified it to a minimum of 1.