Marks: Armor Penetration.
Seals: Crit damage.
Gylphs: Cooldown reduction (per level).
Quintessences: Armor Penetration.

Alternatives:
Seals of Attack speed or Attack damage instead of Crit damage.
Quintessences of Might (atk dmg lv) or Celerity (CD. Reduction per lv) instead of Armor Penetration.

21/0/9
Because building the other Defensive or Utility trees to 21 gives her less pros that the Offensive Tree. Not much to say, it's kinda obviously the reason, she's offensive meele champion and combines pretty well with the build.

Alternativelly you may choose: 21/9/0

Because I did use this way when I was without Marks nor Quintecencess for her, I did focused on mages from my early days on the League. And well because I did found it kinda usefull too (but not a lot) and I actually use Dodge Seals for my Rammus.

This gives some armor and resist, with the Hardiness and the Resistance and some evade+speed with the Evasion and the Nimbleness; but only really efective if you use Ninja Tabi, even more in early game or against auto-attack focused or heavy champions.

I did not recommend a lot, may works kinda well but would ruin the build in some way. One must change the Ionian/Mercury Boots (that are much better for Riven), she needs cd reduction or the tenacity protection. If you wanna try or if you have not the main runnes (for the build) yet.

Start with: Doran's Blade; or Vampiric Scepter; or Cloth Armor + Health potions. Note: you must sell the Lantern before buying the final item.

Ionian Boots: Because the CD Reduction, she doesn't any mana or energy but are pretty dependable on her skills. This will aid you well together with the Gylphs of Celerity.

Wriggle's Lantern: This is good start item, even more if you picked the Vampiric Scepter from the start and good for farming and/or jungling. If you wanna go jungling, I do recommend killing monsters around lv 5 (not from the start) when Riven is more decent and you will have the Madred's Razors.

Youmuu's Ghostblade: Because I did found it pretty decent for mid game (at least); it gives her Attack damage, armor penetration who works well with the Marks and the Quintecensess, crit damage who means more power together with Seals, and the best part Cooldown reduction and the Active Skill who gives movement-speed and attack speed!

Frozen Mallet: I'm not pretending that she will be a tank but HP means survability (from any damage) and more attack damage for your Atma's Impaler also. The passive effect is amazing, every attck you land on an enemy will slow it/them =D

Randuin's Omen: I was about to choose Warmog's Armor for this build, it's pretty good too for Riven (she lacks in regeneration and some hp) but I did read that some people found it not very well for her. The Randuin's Omen gives HP, HP regeneration and pretty decent armor besides the passive and active effects. In resume this item improves more survability and the posibility of either supporting your team in the fights or chasing even better.

Note: You may use the active effect by clicking a key number (depends on the position in your inventory)

Atma's Impaler: At this point it's pretty obious why, the Impaler gives +armor and +critical chance (plus Deadliness mastery and your crit chance Seals). This means more defense and power, togheter with the other items makes good combo and Riven uses her attack power to improve her skills.

The Black Cleaver: Increases the Attack Speed of your champion, even more because you will have the Ghostblade who aids you to land more hits and chasing capability; as result you may use the passive (armor reduction with stacks) more efectively (and even mor if you picked attack speed runnes as alternative). Also gives Attack damage, the most important for Riven combined with the armor penetration of your runnes and masteries to make it even better.

Alternatively: You may sell your Ghostblade for an Infinity Edge at late game, if you wish to have more massive power.

In resume, as you can see all this items makes well combo or aids each other with their effects and the masteries, runnes and passives. =)

The Skill Sequence. Not much to say. It's the most common or popular for Riven builds, if you have a better idea or style feel free to use it.

I do preffer Exaust with Ghost. Because one can chase even better and reduce the defenses of the enemy (thanks to Cripple mastery), and also you can use it to escape and lets your team to kill it better when you are running away.

The Ghost spell very good either for running away from battle and also chasing enemies; or chasing and then turning back (if the tide of battle has changed, for telling example).

Alternatively: Flash instead of Ghost. Or pick Ignite togheter with your Exaust for more offensive capacity.

Teleport are good too, but I preffer Ghost because Riven is focused for battle and one can move well with it in map (even more if you are in the Twisted Tree Map).

I'm not too pro, nor with Riven but I hope this can be of good use for you, or at least you may use this guide (build) as a base or inspiration.

Thank you for reading and rating my build :D