The "+x% Elemental Damage" affix works by adding "x%" of your physical damage to your attack, in the form of the damage type listed.
So, really basic example:
Your physical damage is 100, and the item adds +3% Fire damage.
You gain 3 extra damage to your attacks as Fire damage.
Things this takes into account:
Rings, mojos, orbs (etc) that have an "X-Y" damage affix (e.g. "1-2 Damage")
The base damage range of your weapon, before any elemental damage is added from the affix
+Min or +Max affixes on weapons
(Note: It doesn't benefit from "+X-Y Elemental Damage" affixes on weapons.)
We realize the current wording for this affix can be confusing, and it's something we'd like to make more clear in the future. If you have any suggestions for how this affix could be better worded, we're definitely interested in your suggestions. Just keep in mind that space is limited in item tooltips, and that whatever we use would need to be translated into all of our supported languages.