Resting is changed from the Bioware implementation in several ways.
Without any special treatment your character recovers only their level in hit points when they rest. The amount can be increased as follows:
Where there's a cost the amount is automatically subtracted from your inventory. Read the signage in the relevant areas for costs.
A Campfire will give +2, an inn +5, a healers +10 and a basic level of bandaging IF you are not already bandaged.
This means if you are a lowish level and rest in a healers, most of your damage will be healed for a fairly low cost.
This distance is set to 10m. Any Campfire that will cook meat on it should be valid for this purpose.
To gain the specific benefits you must rest inside the signposted area; usually a Common Room or visible Infirmary area. Simply being on the map does not count. You know you're in the correct area when you see the yellow text, "You have entered a rest location" pop up in your combat log.
Successful use of a healing kit or medicine bag on a PC dresses their wounds and increases their hit point recovery the next time they rest.
If your injured character attends a bardic performance there is a chance that they receive a moral bonus which will increase hit point recovery next rest.
Various things will interrupt your rest; misclicks, crashing, being attacked or party members entering combat. While you will gain none of the benefits of resting you won't have to wait the full 30 minutes before you can try again. You can rest 10 real minutes after an interrupted rest.