How do I unlock the new "Second Wave" options?

Solution 1:

UFOPaedia has a pretty good write up. I'll try to simplify their list, however.

Initially Unlocked

• Damage Roulette - Weapons have a much wider range of damage
• New Economy - The funding offered by individual council members is randomized.
• Not Created Equally - Rookies will have random starting stats.
• Hidden Potential - As a soldier is promoted, their stats will increase randomly.

Unlocked after beating the game on Normal or higher

• Red Fog - Any wounds taken in combat will degrade a soldier's stats for that mission.
• Absolutely Critical - A flanking shot will guarantee a critical hit.
• The Greater Good - The secret of psionics can only be learned by interrogating a psionic alien.
• Marathon - The game takes considerably longer to complete.

Unlocked after beating the game on Classic or higher

• Results Driven - A country will offer less funding as its panic increases.
• High Stakes - The rewards granted for stopping alien abductions are randomized.
• Diminishing Returns - The cost of satellites increases with every one that is built.
• More Than Human - The psionic gift is extremely rare.

Unlocked after beating the game on Impossible

• Total Loss - Lose all gear from soldiers who die in combat.
• War Wariness - Overall funding levels drop inexorably with every month that passes.
• E-115 - Elerium stores will degrade over time.
• Alternate Sources - The power requirements of all facilities are increased.