An "Earth-like planet" in ED is defined as a planet a human can survive on indefinitely out in the open, with no space-suit or environment suit necessary. The necessary conditions:
- Gravity: must be between 0.40 and 2.00 Earth-normal.
- Atmosphere: must have partial pressure of oxygen between about 0.15 and 0.40 atmospheres (haven't done the checking to find the absolute limits here). "Partial pressure" can be derived by multiplying the atmospheric pressure by the oxygen content factor. Total atmospheric pressure must not exceed about 4.2 atmospheres, though this can be exceeded in low-nitrogen, high-argon environments. Edit: And must not have any toxic gases in the atmosphere. Carbon dioxide can be present but levels must be below 0.5%.
- Temperature: must be between 260 K and 320 K.
And that's it. If a planet can be engineered to bring its statistics within these ranges, it is terraformable. The current state of the atmosphere and the presence or absence of a hydrosphere are irrelevant to terraformability; these are considered engineering problems, not laws-of-physics-breaking problems.
As for the actual technology of terraforming, all we really have to go in in lore is the commodity descriptions for terraforming machinery:
Atmospheric processors:
Land enrichment systems:
Together, these indicate that 34th century terraforming tech is a combination of heavy industry and genetic engineering. In "old lore" (the prequel games FE2 and FFE), the Federation tended towards high-tech automated machinery to make a planet as close to Earth as possible, whereas the Empire preferred to use genetic engineering on both the target planet and the cohort of prospective colonists for that planet, so that a planet's terraforming could be completed and people living on it quicker. But this particular aspect of lore now seems to be retconned.