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.