What's the fastest way to raise DPS to 20k as Barbarian
Solution 1:
The easiest way to get a serious boost would be to get a competitive one-hander to use in the offhand, or a two-hander - the problem with that being, of course, that Barbarians in Inferno are already in serious trouble with a shield, even with a load of armor and resists.
The biggest damage booster out there, then (aside from stacking tons of extra strength), would be items with attack speed - by far the most powerful stat when you have a high DPS weapon. Gloves, rings, and amulets are the most common (not sure if they're the only) places to find it.
Substantial amounts of +crit and +crit damage are a little harder to find on otherwise good items, but with the Barbarian's mechanics and passives, they may well pay off.
Solution 2:
There are many things you can do to boost your DPS:
Consider a 2 handed weapon: While sacraficing defense you can boost your base DPS by a significant amount. Luckily, if you find a weapon with high damage, and some vitality you may be able to counteract the lack of defense a bit. Lifesteal/life per kill doesn't hurt either.
Find a shield that boosts DPS: If you're set on a one hander, look for a shield that adds to your strength in order to boost your damage output a bit. A shield can be very defensive and also have offensive properties.
Use gems wisely: This may be an obvious one, but put Rubies in your weapon sockets to boost the overall DPS of the weapon you are using.
Dual wield: The same concept for 2 handers applies here. Increase your damage output significantly by sacraficing some defense.
Use your skills: There are certain skills such as the passive Brawler that can increase your DPS in specific situations. Study your skills and your runes and find a nice balance of crit chance, damage and defense.
Solution 3:
Don't forget about your follower you can do a lot to boost her overall dps which is a boost to yours. Also you need to remember that weapon dps is the biggest increase to your overall dps. It sucks but a higher dps weapon is the way to go. And then the higher your weapon damage the more the other stats effect your dps.