You can obtain Legacy each time you reach level 75. Once you Legacy three times (i.e., level up to 75 four times), you can then start leveling up through ranks 76-100. These are locked for now, but pictures of all ranks and Legacies have been provided to us by lve_msg.
You lose ALL of:
Money
Your money is reset to $10,000 - so if you spend it all before doing Legacy, you actually gain money
Kickbacks
You have to rank up and buy them again
Boosters
You have to rank up, buy them, AND level them up again
ALL Co-op items
Except treasures?
Weapon Mods
You have to rank up and buy them again
You DON'T lose:
Emblems
You keep all the emblem unlocks that you have already bought
Medals
You keep all the medals you've earned
Personal Stats
They are not reset when you legacy
Treasures
You keep all treasures you've gotten, whether or not you've completed the sets for them (not sure if coop treasures are also kept, but they should be)
Guns
All the character weapons you unlock by collecting treasures will be available to you once you reach the level necessary to use the base weapon
For example: to use Marlowe's M9, you must reach level 16 to unlock the base M9 - to use Lazarevic's FAL-SS, you must reach level 50 to unlock the base FAL-SS)
In other words, you do NOT have to re-complete the treasure sets to unlock character weapons again, but you DO need to level up to be able to use them when you Legacy
Taunts
You keep all the taunts you've bought and can use them at any level
Skins
You can use any skin you already own at any level you want when you Legacy
If you Legacy and haven't bought a certain skin, you have to level up to be able to buy it
For example: if you legacy before you buy Marlowe, then you have to level up in order to buy her - if you already bought Marlowe previously, then you can used her even at level 1 when you Legacy
Custom Clothes
You keep all the custom clothes you've bought or unlocked and can use them at any level
You Unlock:

First Legacy:
New rank emblem
4 negative boosters (2 for each slot)
Booster Slot 1:
Out of Breath - sprint recovery time and duration significantly slower - multiplies cash earned from kills 2x
Flat Footed - move significantly slower while aiming - multiplies cash earned from kills 2.5x
Booster Slot 2:
Extra Kickback Costs: medal kickbacks cost 4 more medals to use - multiplies cash earned from kills 2.5x
Small Pockets: you spawn with significantly less ammo - multiplies cash earned from kills 2x
Legacy 1 = 15% increase over base cost
Second Legacy:
New rank emblem
4 more negative boosters (2 more for each slot)
Booster Slot 1:
Slow Healing - health regeneration is significantly slowed - multiplies cash earned from kills 2x
Fewer Grenades - your ability to carry grenades is reduced (eliminated) - multiplies cash earned from kills 3x
Booster Slot 2:
Invalid - you have half health - multiplies cash earned from kills 3.5x
No Power Weapons - you can't pick up power weapons - multiplies cash earned from kills 3x
Legacy 2 = 30% increase over base cost
Third Legacy:
New rank emblem
New skins: clown masks, Doughnut Talbot
Legacy 3 = 45% increase over base cost
Fourth Legacy:
New rank emblem
Possibly more stuff: this is currently locked so we need to wait until ND removes the level cap
Fifth (final) Legacy:
New rank emblem
Possibly more stuff: again, same as above - this is currently locked
Levels 76-100:
These levels have normal rank emblems, essentially continuing from the non-Legacy levels 1-75. Level 100 is a skull emblem. View Them Here
Tips and Tricks:
If you're trying to unlock treasure sets with Treasure Hunter, do it before you go into Legacy (except for Hardcore treasure sets, obviously, because there are no boosters in Hardcore mode)
Spend all your cash on skins, emblems, custom clothes, and taunts before doing Legacy - if you want to buy everything, do it before you Legacy, so you can spend all your Legacy cash on useful things like kickbacks, mods, and of course boosters
Using Sugar Buddy (with a good buddy) and Deposit (leveled up if possible) will get you more cash faster than using Negative boosters - plus you won't have a handicap