First things first, you can check out the d20 Open Gaming License (OGL) System Reference Document (SRD) for free at the following locations:
Download, read, understand. It's all free (and legal).
What Conan has done is use the above documents as the starting point, then made some changes.
Conan replaces the SRD classes with new classes with powers and abilities that more closely match the Conan mileu.
d20 armor adds to a character's armor class, making them harder to hit. Conan armor does not make the character harder to hit, but subtracts from damage dealt.
In d20, your armor and possessions and base DEX make you harder to hit. It is assumed that as you rise in level, you get better armor and possessions. Conan assumes the character has few possessions and little magic, therefore all characters have a Defense Bonus based on their level, which makes them harder to hit.
Because armor reduces damage, all Conan weapons do more damage. A general rule is to up the dice one size. d4 becomes d6. d6 becomes d8. d8 becomes d10. d10 becomes d12. d12 becomes 2d8. d20 becomes 2d12.
Also, because armor reduces damage, it takes a lot longer to take down an opponent than in plain d20. Therefore, Conan introduces Armor Piercing and Finesse rules. All weapons have an Armor Piercing value. If your STR bonus + AP value is more than the armor's Damage Reduction (DR), the DR of the armor is halved. Example, your STR bonus is +3 plus the AP of your weapon is 2 equals 5. The target's armor DR is only 4. 5 beats 4 so the armor only blocks 2 pts of damage.
Certain weapons are labelled finesse weapons. For these weapons, you use DEX instead of STR to roll to hit. If your to-hit roll with a finesse weapon beats the target number by a value greater than the DR of the armor, the DR of the armor is completely ignored. Example, you're fighting with a Finesse weapon. You need to roll a 13 to hit an opponent with DR 4 armor. You roll 19, which beats 13 by 6, which is greater than the DR 4. Your attack completely ignores the target's armor and the target subtracts nothing from the damage rolled.
These two rules balance out the extra time it takes to take down an opponent using the DR rules.
d20 offers easy access to healing magic. Conan does not have easy healing magic, therefore many of the classes have more hit points in the form of higher dice sizes.
d20 Initiative is just DEX modifier + any feats. Conan Initiative is DEX mod + REF save bonus + any feats, allowing characters of higher level to have higher Initiative.
d20 provides a single stat increase every 4 levels. Conan provides an additional increase to ALL stats every 6 levels.
d20 magic is common and easily available and cast and have a completely different system than Conan, which assumes that magic is uncommon and difficult to cast.
There might be some other minor differences, but those are the big ones.
When importing weapons from other d20 games, increase damage by 1 die size (see above).
When importing armor from other d20 games, compare AC bonus to other equivalent armor in Conan to determine appropriate Damage Reduction.
When importing NPCs from other d20 games, increase their INIT by their REF save bonus and given them a Defense Bonus equal to an equivalent class in Conan. Fighter = Soldier. Cleric = Scholar. Rogue = Thief. etc. Remove Armor bonus from their AC and add their Defense Bonus from their class. Increase weapon damage (see above) and possibly hit points.
When importing monsters from other d20 games, increase their INIT by their REF save bonus. Remove natural armor from their AC. Divide natural Damage Reduction by 5 and round up. Increase all damage by 1 die size (see above).