DPS, or damage per second, is a calculation given by your damage and attack speed. The formula is:
Damage * Attack * (227/Attack)^2 / 56.75
For example, with the Training Sword at level 1 and no other bonuses:
20 * 227 * (227/227)^2 / 56.75 = 80, exactly as shown on the character sheet.
The final number will be rounded up, to match the number displayed on the main page character sheet. There is some other rounding, but this calculation will get you within a few dps of the final number. (?)
Damage is a tough number to find. It is the damage from your weapon, plus any skills or accessories, plus any bonuses from perk levels, plus any bonuses from Gladiator's Coin, plus any bonuses from pets.