Akali isn't really a hard champ. She's more about decision making than mechanics. Barely any mechanical skill is needed to play her.
So when you start, you're going to want to see who you're laning against. If it's an AD guy like Zed or Talon or Yasuo, take cloth + 5. Most AP matchups benefit from boots 4, especially the xerath one you mentioned. If you're good at dodging skillshots, boots + 4 can be played in to Zed as well. Longsword + 3 is also a viable start if you wouldn't benefit from the other two items, but in most matchups the other two will help more.
During your pre-6 laning phase, you want to just farm. You're pretty weak in comparison to many other mids who already have long range poke, so you'll just want to kind of stay out of the way unless you see a good opportunity where they've already burned an important cooldown. Pretty much everyone will outpush you until you get E, so you kind of have to accept that you won't have any level advantage. Remember to CS with Q when it'd be too dangerous to get in and just AA the minion. It's a short enough cooldown you should be able to stay safe and get most of the minions. During this time, you normally level QWQE and then its R> Q> E> W. The order of the first 4 can change but that's generally the best.
First back, I prefer revolver if I have 1200+ gold. It's sustain is really nice. If you got forced out of lane before you got enough gold, vampiric scepter can replace it for sustain. Either item in gunblade's build path gives plenty of damage so that's fine. Once you're level 6, your ult will start stacking. You generally want to wait until you've got two stacks to mess around too much, but if you see a good opportunity, don't be afraid to go for it. After you have a couple of stacks, land a Q on them, wait until Q's cooldown is almost all the way gone and R to them. Then AA, E and land another Q. From here you can either continue the engage or back off a little. Shroud takes a lot of energy so don't blindly cast it. If you backed off and they're not dead, do the same thing again. Remember, you still have a Q on them so they have some unexpected damage waiting. A lot of the time this will give you a kill at 6. If you can't get a kill in lane, push the lane out and roam. You want to get a few kills. In small form, your combo is Q-R-(hextech)-AA-E-(repeat).
Once people start grouping, try to pick off anyone out of position. By this time you will probably have Zhonyas, don't forget the active. In teamfights, you'll normally want to wait for an initation and pick off lower heath/squishy targets when you can. If your team doesn't have an initation, you can try to quickly get in, take out a squishy and Zhonyas. I don't like starting fights like this but I've seen it work.
For a general build path, I start like I said above, rushing gunblade. If you're taking a lot of heavy damage, an early Seakers Armguard or Negatrons can help. Second, you generally want finish Zhonyas. Against crazy burst like Zed an early Zhonyas can help. I would try to get at least a revolver or vampiric scepter before it though. After Zhonyas, I generally build Rabadons, Void Staff and Guardian Angel, in that order. MPen boots can be put somewhere in there depending on when you feel you need them. In a heavy AP team, Abyssal Scepter can replace Void Staff.
Good luck man!