All of this assumes that you are responsible for keeping Mangle up yourself. If you have another druid or an arms warrior keeping a bleed damage debuff up, you can obviously mostly ignore your Mangle button. All of this also assumes that you have a DPS spec which includes 2/2 Stampede and 2/2 Predatory Strikes.
Step 1 of DPS is to let the tank get aggro. If they get a parry right off the bat and you open up, you end up thinly pasted on the floor.
Assuming you are able to, you should Feral Charge into position (to get Stampede up) and start your cycle. Do not bother with stealth at all.
Get Feral FF up as soon as possible. It is identical to fully stacked Sunder Armor, and with a proper spec, it costs you 0 energy and 1 GCD.
Get Rip up as soon as possible, I recommend opening with Mangle, Shred, Tiger's Fury, Ravage then Rake. If you do not have 5 CPs at this point, Shred. Rip once you are at 5 cps. Get Savage Roar up after your next combo point builder. Assuming you did not get the Feral Charge off, just replace the Ravage with a Shred.
Trash DPS - single-target
Single-target trash is all about burst. Once you have Roar up, make sure Rake is up, and spam Shred, using Tiger's Fury whenever it's up. At 5 points, judge how long your target will live - use Rip if it'll be up a while, or Ferocious Bite if it will die soon.
Trash DPS - AOE
On the occasions where you will use AOE, you use Swipe.
You still should get Roar up as white damage is a large fraction of a Druid's DPS. Once Roar is up, just spam Swipe - Cat wantonly, again using Tiger's Fury to replenish energy as you can. Be careful, it's easy to pull mobs that are being AOE-tanked, AOE trash is the prime cause of death of raiding cats.
Use Berserk at the start of big pulls whenever it's up, but don't use it on the pull right before a boss.
Simple version is, once you've got the mob debuffed as described under "opening", your next objective is to get any number of combo points and then Savage Roar. At this point, depending on how much time is left on Rake, you might want to pool a little energy so you can refresh Rake right before it falls off, or you might Shred again, then pool for Rake refresh. Either way, Shred and Rake appropriately to 5 combo points again. If you have a lot of time left on Rip and Savage Roar, Bite. Otherwise refresh as appropriate. From here you will most likely end up weaving Rips and Roar, and repeating until the boss's health drops below 25%. At this point, Blood in the Water kicks in, and using Ferocious Bite will refresh Rip, so you start using Ferocious Bite instead of Rip, unless Rip happens to fall off (and it shouldn't).
- Keep Feral FF up, unless you have someone else responsible for the debuff in the group
- Keep Mangle up, unless you have a bear or arms warrior in the group
- Keep a 5-point Rip up, and try to apply it when Tiger's Fury is up if possible, but do not trade more than 3.3 seconds worth of uptime for this.
- Keep Savage Roar up
- Use Ferocious Bite when Blood in the Water is active since it will refresh Rip
- Keep Rake up, if Tiger's Fury and Rake refresh happens to line up, Rake with the Tiger's Fury buff up
- Use Shred for combo points
- Use Tiger's Fury on the cooldown
Berserk is kind of a complicated animal to use perfectly. It's perfectly adequate just to use it on the cooldown, though.
- Try to Berserk with about 80 energy, depending on latency. You'll regenerate another 10 during the global cooldown, and can then start spamming abilities with close to 100 energy.
- Don't Berserk with Tiger's Fury available, or about to become available in the next 15 seconds, as Berserk prevents use of Tiger's Fury.
- While Berserk, you should mostly use Shred. Refresh Rip, Rake, Mangle, and Roar should any of them expire, but otherwise continue to spam Shred, even once you reach 5 combo points. Unlike in WotlK, you can use Ferocious Bite while Berserk is up assuming it won't adversely affect bleed or SR uptime.
- On a fight less than 3 minutes long, you should save Berserk until the end if the boss has a low-health enrage, to help power it down during the dangerous phase quickly.
- On a fight more than 3 minutes, use Berserk as soon as the tank has a safe aggro lead. This should allow you to use it again before the end of the fight.
- Because Berserk only affects yellow damage, and Bloodlust/Heroism only affects white damage, it doesn't particularly make any difference whether you use Berserk at the same time as Bloodlust or not.
- You should try to use Berserk when your best procs are active. This frequently occurs right at the start of the fight.
1 - On Clearcasting procs, always Shred. Always. Unless Mangle is actually down, then Mangle.
2 - If possible, try to apply bleeds when Tiger's Fury is up, as their damage is calculated the moment they are applied, not on the fly. If you Rip without Tiger's Fury up, then Tiger's Fury, Rip's damage does not increase. If you Rip with Tiger's Fury up, Rip's damage stays the same when Tiger's Fury falls off. Mangle, however, will change the damage of bleeds if it is applied or falls off after they are already ticking.
3 - If you find yourself with 5 combo points, plenty of time left on Roar, and Rip still at at least half duration or so, you can use Ferocious Bite to dump combo points. The amount of energy that you do this at does not matter as long as it does not adversely affect Roar/Rip/Rake uptime. Early on you won't be able to do this at all, as your crit improves you'll be able to fit it in occasionally, although it still won't be frequent. On fights with a crit-increasing gimmick such as Loatheb, however, you can do it practically every cycle.
4 - If you find yourself in a situation similar to the above, but in which you do not have enough time on one of your timers to comfortably use ferocious bite without crashing your cycles, just hang out and only do enough to keep yourself from hitting full energy. Refresh Mangle or Rake if they drop, or just Shred to keep your energy under about 80. Wasting a couple combo points is a far lesser sin than wasting energy regen.
5 - Take a deep breath and relax. The path to the greatest DPS is not to spam abilities, but to wait patiently. Don't Shred unless you get up over 60-ish energy. If, while waiting to get there, a timer comes up for renewal, renew it. If you just mash Shred every time you have 40 energy, you can end up waiting several seconds for enough energy to reapply a Rake or a Mangle, and suffer a DPS loss. Careful planning and lots of practice on target dummies are important.
6 - If you have fairly low energy, Rake has dropped, and Rip is about to drop, but you haven't shredded 3 times on this Rip (mods like Droodfocus and Badkitty provide Shred counters), you should Shred rather than refreshing Rake.
7 - Berserk is often best used between 0 and 15 seconds after Tiger's Fury. It no longer removes the +damage effect if used immediately after TF, so stacking them is perfectly acceptable, so you want to use it in the window between TF's going on cooldown, and the ability coming off cooldown again.