Pull up your PIP Boy menu and click on the little bell shaped button next to the date. That will bring up another menu where you pick how long to rest/heal.
Ten minutes is the shortest, I believe. Then certain numbers of hours followed by times the next day if you want to jump to certain times rather than stare at the screen for awhile.
Alternatively, you could go spend money (gasps in shock at the idea

) at a hotel. Renting rooms lets you sleep for about 8 hours, time enough to heal a few hp's.
There's not a hotkey I know of because of the control you have over how long you sleep. If you are injured when you pull up the menu, it will give you the option to "rest until healed". If one or more NPC's are injured another option of "rest until party heals" pops up. WARNING!!! If your really badly shot up after a random encounter, you may be resting for days to weeks! So be careful when doing timed quests!
Hope that helps. That's all I can remember off the top of my head.