Kayle is one of the more unique champions in the game, in that she can build ANY offensive stat and get something out of it (Much like Jax!). On the flipside, she doesn't get much out of tanky stats, other than like the armor from zhonya's or MR from Abyssal Scepter or Wit's End.
The most important thing to know about Kayle, though, is how to use her ultimate. Typically you won't be using it to save lives that are almost lost. That 25 HP adc will appreciate living for three more seconds, but then they die right after, and there you are without an ult. The best use of Kayle's ult is preventing damage from occurring at all, usually at the start of a team fight right before the enemy team unloads everything onto their primary target.
In most builds you'll want to have attack speed in some form, even if it's not your primary goal. The reason for this is that her E is where most of her damage comes from, and since that is based on auto-attacking, the more you auto-attack the more damage you can do! (It also helps stack up her passive faster).
Now for builds. The primary place I take Kayle is in the jungle, and there I prefer to go with a more attack speed oriented build based around the Devourer enchant. (Also, I should point out here in most builds you will max E first, as with attack speed it is your primary damage source) Anyway. My build path typically looks like this in the jungle:
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(depending on what I need the most). This gives Kayle CRAZY attack speed, and thanks to hurricane's AoE you can melt entire teams like this. It also gives you 40% CDR, which means your ult is up almost constantly. Also of note is that your E will have 100% uptime, which means you can stay in range at all times.
Kayle can also be built AD, and this build is more typical of any adc/marksman/bruiser build. You won't be getting Hydra, generally, as even though Kayle is sometimes a melee champion, this is typically when she is waiting for E to go off CD and re-positioning herself. You should not ever be in melee range, is basically what I mean here.
Kayle's can also focus on a more typical AP build, but even in this case you'll still want to have AT LEAST a nashor's tooth for the cooldown reduction and attack speed that synergizes so well with her kit. Often your build will look more like a typical mage:
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(again, whatever you need here, basically) or something like that. I am personally of the belief that runaan's hurricane is still a great addition to this build, but you can probably live without it if you prefer a burstier build. It's bascially the difference between dealing tons of damage with each swing or dealing smaller damage, but in an AOE really fast. It's all about what you prefer!