This guide shows you how to build Master Yi as a melee AD bruiser/caster.

AD to empower your Q, and to give you added auto-attack power while in melee.
Armor and magic resist runes to reduce incoming damage, especially when your meditate's down.

Offense because three fourths of your kit is damage-based, and because Yi's ratios and kit are worth it.

Defense in the rest because you want to reduce damage to stay alive and be effective.

All cheap AD items that're easy to farm and build. Lots of life steal and defense to stay alive while bruising and casting your Q. Mercury's Treads are great for countering those pesky mages, sunfire capes, and some melee champions who inherently deal some magic damage. Feel free to get Ninja Tabi boots instead if you feel that enemy ad champions are becoming problematic. You may also want to ditch GA for a stronger armor item like Randuins Omen or Frozen Heart.

Q is your bread and butter ranged damage spell. Most reliable damage skill in his kit.
W is okay as long as you put one point in it, but I recommend you max this last as it otherwise takes away from your overall dps, and can be interrupted by cc [hence unreliable].
E is great for added autos with true damage!
R. Invest when points available. This lets you close the gap to barrage a target with auto-attacks, and/or is great for escaping when needed.

Flash is great for both getting in range for scoring a killing blow with your Q, and/or escaping over a wall.
Ignite for the added damage and anti-sustain versus those pesky ad carries and their massive lifesteal.
Exhaust and Ghost are the only two situational spells I'd take. Everything else just doesn't get my attention due to it's lack of effectiveness.

Bruise and cast your Q damage. Build cheap AD items, and become tanky. Feel free to try other items. Don't limit yourself to just my build, but definitely try to get some synergy like in this guide, where the theme is burst plus bruising damage, and tankiness.

PROs:
Strong Q damage.
Tanky as hell.
Scales well into late game.

CONs:
Not a glass cannon hyper-damage build.
Can still die relatively fast in a 1 v 2-5, especially if you're not ahead.
Has no kit-based CC, and can be easily countered with knock-ups and suppression.