First, tons of molten nickel/iron (mined from M-type asteroids) and decaying radioactive elements are injected into the core through various drill sites, to restart the magnetic field dynamo. Then Vesta is covered with a sealed world-dome of a super strong but clear material (preferably self repairing) held up by columns in place of the drill sites. Next, thermonuclear detonations and focused solar mirrors could outgass carbon dioxide and oxygen, directly from the compounds in the regolith. As a thin atmosphere forms, strong greenhouse gases can be pumped in to heat the asteroid enough to melt any underground ice deposits. It is likely more air and water would be needed (this depends on the volume of the enclosed worldhouse), so nearby comets or astroids could be mined for volatiles. Buffer gases like Nitrogen or Argon are harder to come by, may need to be exported from the the outer dolar system. Eventually droplets of water (likely beachball sized in the low-G) may condense on the worldhouse roof and fall as rain, turning craters and troughs into lakes and rivers. Once the regolith oxidises and settles, genetically modified bacteria, algae, and eventually plants and animals, can introduced to form a biosphere.
A project like this could only be feasible in the far future, but turning Vesta into a garden world could help miners of the asteroid belt become less dependent on food from Earth or Mars, or simply act as a reserve of species.