This is the Guide to how overpowered Despair really is. Everything in the build is connected with each other and at the end i will give you some statistics on its strength.

For Marks and Glyphs you should take magic penetration, while for Seals you can take ether defensive stuff (best is Seal of Scaling Armor as it also scales with the 'Enhanced Armor' mastery), or you can take ability power to increase damage on Tantrum and Bandage Toss.

With Masteries you can pretty much take what you want but i think that this is the best mastery as it has many features that combine with each other:

OFFENCE:
Sorcery - Useful for tantrum, as then when you get hit, you can use it every 2secs or so.
Expose Weakness - With despair allies will always deal 1% damage more.
Mental Force - Extra damage is always handy.
Spell Weaving - Combines well with his passive to deal even more damage with despair.
Executioner - Despair does constant damage, so you need the mastery for better finishing.
Archmage - Always welcome extra AP.
Dangerous Game - Also works with assists and with despair just standing there assists.
Devestating Strikes - Even more magic penetration (see runes and items).
Arcane Blade - Also triggers the Morellonomicon when despair can't.
Havoc - Even more damage, muahahahahaha.

DEFENSE:
Block - Good combined with tantrum.
Enhanced Armor - For less squishy-ness, since despair is DOT.
Unyielding - Defense against champions is always useful, also pairs with tantrum and block.
Veteren Scars - Just as a filler for the next tier.
Oppression - Awesome with despair-Rylai's Crystal Scepter combo.

START:
Crystalline Flask: Infinite Health and Mana potions. Handy in the beginning to farm longer and to make up for the high mana cost of despair.

RETURN:
Tear of the Goddess: Buy this as fast as possible! The instant +250 mana together with the crystalline flask makes sure that you will have enough mana for despair. As you get higher level and your bandage toss and ultimate get more expensive and time elapses you will get more mana. Since despair will be on most of the time in combat, you will get +5 mana almost every 8 seconds. So in 20 minutes you will have the +1000 mana the tear gives you. If you want a reference: the base mana Amumu has at level 18 is 967.

MUST HAVE:
Rylai's Crystal Scepter: It gives +400 health and makes sure Oppression is always triggered making you more survivable. It gives +100 AP which equals +1% of the enemies health as damage to despair and it makes sure the next item is always triggered: Liandry's Torment.

Liandry's Torment: With Rylai's Scepter triggering the effect and the +50AP, this item gives +4,5% extra damage to despair. And with its 15 magic penetration that combines well with the runes and Amumu's passive, it gives an extra boost to damage. there also +300 health for extra life.

RECOMMENDED FILLERS:
Morellonomicon: +80AP for extra damage, +20% cooldown reduction (good with sorcery and tantrum), +100 mana regen so that despair drains mana slower and its passive is always triggered with despair making it harder for enemy champions to survive (good combined with executioner).

Will of the Ancients: +80AP for extra damage, +20% cooldown reduction (good with morellonomicon, sorcery and tantrum), 20% Spellvamp: while its is actually only 6,66...% for AOE spells it is still a lot considering despair can easily do 15% of each enemies health damage per second.

Rabadon's Deathcap: Replace Crystalline flask for it in late game. +120AP for extra damage, +30%AP for an item that gives off the charts amounts of AP.

POSSIBLE FILLERS:
If still requiring extra mana, consider Micheal's Crucible or Athena's Unholy Grail.

If needing extra damage you can take Abyssal Scepter or Void Staff with lots of magic penetration and AP.

For movement, it is best to take Sorcerer's Boots with an enchantment of choice.

For even more defense and a slight extra AOE magic damage, take Sunfire Cape.

Other useful items for their active abilities and flat AP are: Deathfire Grasp or Blackfire Torch.

Take despair and curse of the sad mummy when you can. In between you can chose i usually try to max out tantrum fast for its passive and it does AOE damage, but i do put a single point in bandage toss early just for catching up with enemies that run away.

You can play with almost anything, i like flash and heal although you could take clarity for the mana need in the beginning (for mid and late game, its pretty useless). The other useful spells are exhaust (to chase and reduce damage income), ghost (for movement even though I prefer flash for that), barrier (for more defense although heal is better and while taking heal and barrier is powerful maybe a different spell is better) and ignite (for pure damage over time that adds up great with your despair damage).

So if you take the runes I said(with AP not armor), the masteries I chose and the items I recommended, then these are your stats at level 18:

Item cost: 14500g
Auto-attacks: about 130 - 150 damage of which 25 - 30 is magic damage
Bandage Toss: About 770 magic damage (*Or 810 when enemy is under 50% health)
Despair: About 40 magic damage/second + 13% of the enemies health/second (*Or 14%)
Tantrum: About 490 magic damage (*Or 515)
Curse of the Sad Mummy: About 850 magic damage (*Or 900)
Max Magic Penetration: 60
Health: About 2700
Mana: About 2000
Mana Regeneration: 32/5s = 6,4/s (Despair only drains 1,6 mana/s
Cooldown Reduction: 35%
Spell Vamp: 20% = about 0,9% of each enemies health per second with despair on.
Physical Damage Reduction: 48%
Magical Damage Reduction: 37%

So by just auto attacking with despair on, you will probably kill your foe in 6-7 seconds.
If you use tantrum twice, it will take 4-5 seconds.
If you add a bandage toss, 3-4 seconds.
And he will heal 50% less
And be slowed for 15%
Good?...