How are “Days” determined for Warframe login rewards

If you're here from the future, the damage calculator pointed out by Oblivious Sage is outdated as of Damage 2.0. Warframe's wikia site has an up-to-date, extensive paragraph on damage calculation, along with formulas.

The system is quite complex, but the gist is:

• Enemies (and NPCs, and warframes) are made of "health materials" - ie. different types of health, shields and armor.
• Every "health material" applies different multiplier against different damage types.
• When you attack, the final damage within your attack is calculated separately for each damage type.
  • Health is a plain, old health bar. If it's depleted, the enemy dies.
  • Shields is a separate health bar that serves as a protection for health bar. If it's depleted, the damage goes to health.
  • Armor is not a health bar. It adds its own multipliers on top of health's multiplier (cumulatively) and reduces damage the health takes. However,
    • the more armor the enemy has, the more weight armor's multiplier has over health's multiplier,
    • damage types strong against armor reduce that protection (dealing more damage), while damage types weak against armor increase that protection (dealing less damage) - on top of the damage multiplier.

You roll by simply tapping the sprint button once (shift by default).