This build focuses on Damage per Second (DPS) as well as Ability Power (AP). Kayle is a very versatile champion and can take other roles as well. Being an All-Around type character, Kayle has skills that make her like a support champion but pushing skills as well. Despite mana being a disadvantage for her, there are many ways to make it up in the game. I welcome any tips or comments anyone has, thanks!

Greater Mark of Insight (9)- Increased Magic Penetration by 8.55

Greater Seal of Clarity (9)- Increased Mana Regen (16.2 / 5 secs. @ level 18)

Greater Glyph of Celerity (9)- Cooldown Reduction (CDR) by 8.1 @ level 18

Greater Quint(essence) of Insight (3)- Increased Ability Power (AP) by 5.67
Feel free to change according to what you need for a match

This build uses a 21-0-9 mastery tree, which focuses mostly on strength, but considers utility for mana regen and such, cuz Kayle definitely needs a lot of mana.

Strength:

Deadliness: 1
Archmage's Savvy: 3
Sorcery: 4
Alacrity: 4
Burning Embers: 1
Archaic Knowledge: 1
Brute Force: 3
Lethality: 3
Havoc: 1

Utility:

Good Hands: 1
Perseverance: 3
Expanded Mind: 4
Meditation: 1

Early Game:
Start by purchasing Boots of Speed and a Health Potion if you want. Try not to return back to base until necessary, but rather, stay in lane and try to only level up off minions unless you feel ambitious enough to go for kills. Upon getting enough gold, return to base by recall and buy the Sorcerer's Shoes or any other shoes that you think would be better for a specific match and buy Blasting Wand to begin Guinsoo's Rageblade. Finish Guinsoo's Rageblade when you have enough and buy Fiendish Codex for Deathfire. Finish Deathfire Grasp and by this point, you will be well into the game
Mid-Game:
Buy Stinger and you may decide to defeat the Ancient Golem for it's mana regen buff (only in Summoner's Rift), maybe even earlier. Finish Nashor's Tooth for 50 Attack Speed and more mana regen. Start Lich Bane by buying Blasting Wand. Remember, Kayle is more built towards support and pushing, so try not to chase or get ganked more than once.
End-Game:
You will be a definite support champion and pusher by now, but you may have a few kills if you've been fed or you ganked with a tank. Finish Lich Bane, and continue to defeat the Golem and act as a support and pusher. Start Zhonya's Ring (Zhonya's Hourglass or Rabadon's Deathcap rather, because of the patch) and continue until the end of the match.

Holy Fervor: Kayle's Champion Skill, 30% of AD is added to AP and 15% of AP is added to AD

Reckoning: Attack Skill, can be used for taunting, can slow, can take down enemies early game if used with timing

Divine Blessing: Healing/Support Skill, can be used to help others escape or not get killed, increases target's movement for 10 seconds, as well

Righteous Fury: Attack Skill, gives Kayle range with auto-attacks, has splash damage and can be used to cut down mobs of minions quickly

Intervention: Ultimate Skill, immunity for certain period, can be used to escape time-based skills or deaths, very useful when used correctly on team members at right time

Clarity

Restores mana, very useful for Kayle especially because she can run out of mana very easily if wasted

Ignite

Deals 50 base damage plus additional "burn" damage over time. Is not as effective later in game, but useful early-game when Kayle is not as strong yet