I might have to make this into a proper guide at some point, given how much there is.
RUNES:
Precision/Resolve, almost always. Even in winning lanes. There just aren't enough good options for Kled in any of the other trees.
In Precision:
Press The Attack
Triumph
Legend: Alacrity
Coup De Grace
In Resolve, for hard lanes:
Iron Skin/Mirror Shield
Second Wind
In Resolve, for easy lanes:
Demolish
Conditioning
The Tenacity granting runes in both trees are situationally good if the enemy team has a lot of CC that can be reduced by tenacity. A lot of this is subject to change once they get around to nerfing the more obviously broken runes (Triumph and Coup, particularly), but this should serve you well for now.
ITEMS:
- You build this every game, first or second item. First most of the time, second only if the enemy laner is very squishy, in which case the burst provided by a Hydra item might be more valuable.
- You build one of these almost every game. Titanic is the one you should probably go more often, but go for Ravenous if you're ahead and snowballing against a squishy.
- If the enemy team is tank-heavy, you buy this instead of a Hydra. The lack of waveclear will be noticeable, but its not impossible without them, and BoRK is almost a requirement to be able to damage tanks after a certain point.
- Generally good item for Kled that you buy almost every game.
- You're always going for defensive boots. None of the offensive boots give stats that Kled really finds valuable, at least not enough to not have Tabi or Mercs.
- Most games you'll get GA, but Mercurial is a suitable replacement if the enemy team is really heavily AP.
- Your final slot, though not necessarily the last item you build
- Because sometimes you have to.
Typical final build:

Ability max order: R > Q > W > E.
You want to be aggressive early. You are very strong levels 2-5. Level 1 trades aren't that great because its hard to remount without W. Level 6 trades aren't that great because you don't have a real level 6 powerspike. Play around your W cooldown for the most part. Try to trade when its up, or right when its about to be up. You can use your Q for poke, but the majority of its damage is backloaded so be sure to utilize the threat of that damage to zone enemies. If you land Q and W is up or about to be up, you should go in with E. You almost always will win that trade.
When it comes to pushing, remember that your E will clump up minions, and that your Q does bonus damage to minions. This makes Kled's push without Tiamat not that abysmal, which is what allows BoRK to be an item choice, though of course the E minion clump also synergizes incredibly well with Tiamat, so be sure to use that when splitpushing.
MATCHUPS:
The matchups that I have historically had problems with as Kled are:

Fiora straight up outdamages Kled at all points in the game, and a large portion of that damage is %HP, which especially shits on Kled. Its the easiest thing in the world for Fiora to parry Kled's mounted Q, and parry also shits on Kled while unmounted because it prevents him from gaining Courage and also can slow his attack speed. Not sure how this matchup goes in preseason. I'd imagine its a little more in Kled's favor as he was less effected by the loss of the old runes, and benefits more from the new runes than Fiora does, but still a matchup to look out for. Tips for beating her: disengage when she Ws your Q - yours has a shorter cooldown. Try to take some trades without using Q at all. If you dismount, back.
Shen is pretty similar to Fiora - does a lot of %HP damage, can prevent Kled from regaining Courage. Rather than win by outdamaging you however, Shen wins by blocking most of your damage output. He will EQW you, all your W autos will be blocked by his W, and you will cry. Try to dodge his E with yours, ask for jungler help, play relatively safe and back if you dismount. With the new runes I'd take Demolish and try to hard push when he ults or TPs away.
Teemo is a feast or famine lane. Its heavily in his favor but if you can get an early kill on him you just outright win. Don't auto him until the blind wears off so that you don't waste W. The goal here really is to not take too much damage level 1/2, and all in him level 2/3. Take Mirror Shield and Second Wind. Probably back if you dismount.
I want to make it clear since I've said to back if dismounted for these bad matchups - in many cases, backing when dismounted is a bad idea. Its just that if you are against a champion who can prevent you from gaining courage through blocks or blinds, or against a champion who can easily burst you down while unmounted, and you have the chance to back, you should, because if you stay their cooldowns will come back and they will all-in you while you can't run and you will die.
If you have other questions feel free to ask.