League of Legends (LoL)

Well for runes I normally go:
armor pen red
flat armor yellow
mr per level blue
move speed quints

masteries 0/21/9

summoner spells I'd go with heal/ignite/tele/ghost/flah. I have taken a great liking to heal ignite, very much. But that's my personal preference. Before that I used to always run tele/ghost. It's all situational tbh. Exhaust is meh, I'd only take it if your team lacks it.

Most guides and people will say rush trinty force on her. And while it is a god-tier item for irelia I wouldn't say it's mandatory. If you look at the picture I posted I did not have trinity. I WOULD have liked trinity, but I did not trust our shen to use shureylas. So I kept mine, otherwise I would have subbed it out. Just try to build as situationally as possible. Most of the time you'll start cloth 5 or regrowth pendant. Usually I get wriggles and mercs/tabi as my first items. If I think I'm going to spend the next 20 minutes farming or it's going to be a long laning phase I'll pick up a gp5 or 2. You should pick up an early phage. probably after wriggle. If you're up against ap top like rumble, you should pick up a wits end.
for mr I'd go force of nature or wits end
for armor I'd go randuins or thornmail
for damage I'd go atmas trinty
for more cc frozen mallet
for utility shurelyas (esp if you dont have ghost and your support isnt building one fast enough for team fights)
General bulkiness aegis guardian angel warmogs. I rarely ever get warmogs though. not a bad item though.

Set set some goals for yourself. I try to get 100 cs by 13 minutes. You'll probably always level w up first. Last hitting at tower for the caster minions let the tower hit them twice then hit them then bladsurge or you can just active w and hit them once after the tower hits them twice. If you go trinity, try to get the most out of trinity procs. R hit hitt r hit hit r ect. Your bladesurge auto procs trinity blah blah blah. Use bladesurge to kite or close gaps by dashing to near dead minions. You are a tanky bruiser assassin, jump on their carries eat them. Proceed to next priority.

Arctic Warfare Caitlyn
Aviator Irelia and Infiltrator Irelia
Tempest Janna
Prestigious Leblanc
Traditional Lee singer
Sorceress Lux
Cowgirl Miss Fortune
Blade Mistress Morgana
Pharaoh Nasus
Haunting Nocturne
Iron scale and bone claw Shyvana
Riot Squad Singed
Highland Tryndamere
Aristocrat Vayne