Followers gain a 2.5x multiplier to base stats on items (Str, Dex, Int, Vitality). This is because they are only able to equip jewelry and weapons - in order for their stats to remain competitive with more difficult monsters, they need the boost. In addition, they contribute to the hero's Magic and Gold Find, as well as Bonus XP, but only at a 0.2 multiplier - so, if your follower doesn't need the additional power, you can use them as a way to stack some extra +loot items and benefit that way.
Other item stats, such as +damage and on-hit effects work as normal.
From the standpoint of your weapon: Weapon Damage is king. Above all else, you want the highest possible amount of raw damage and DPS possible. Beyond that, you'll want to take a look at this formula to understand the value of other stats.
In short: at low levels, nothing is going to beat raw +Damage on any slot where you can get it (Rings, Neck, Offhand). As you increase in level, you'll eventually reach a point of inflection where the multiplicative scaling gained from adding +Dex is more valuable than the straight + Damage. This point of inflection will vary with other stats, and particularly with the base DPS of your weapon - your best bet is to simply keep an eye on the +Damage portion of the tooltip when comparing items.
As for stats like Crit and Attack Speed, the same basic rules apply. In general, .1 attack speed is worth 10 Dex, but this ignores the defensive benefits of Dexterity, and since attack speed bonuses are provided as percentage multipliers, you'll need to do some math. You'll need to run similar calculations with +Crit and +Crit Damage, but in general, unless you use skills or passives that rely on Crit, you can assume those stats are less valuable than the others.
Really, all of this comes back to one key point: Trust the Damage Stat on your Character Sheet. So long as you're doing the basics right (using a level appropriate, high DPS weapon), it isn't going to steer you far wrong. Beyond that, Dexterity is King, and everything else depends entirely on the magnitude of the stat that you get. An item with +Crit might be better than an item with +Attack Speed, based purely on how much of it is there.
Best Answer
I believe only the primary stats get the multiplier for followers.
You can always view the effect of stats and damage multipliers by seeing how the "damage" number changes in your follower's popup window as you equip and unequip gear from them.
In general though, most people feel that after normal difficulty, it is not effective to equip your followers for damage, as yous will quickly outpace theirs. You may get more bang for your buck by giving them +vitality and defensive stats, so they survive longer to help you with their special abilities, and giving them magic find and gold find and +exp, which carry over to your character.