Terraform
The terraforming feature allows players to add five fields to a planet.
It will normally be necessary to buy the Terraform Planet option from the store, for 35,000 credits.
On exceptionally rare occasions, the Terraform Planet option can be won from the daily lottery, but terraform options won in this way do not work on planets that already have 320 fields.
advantages and disadvantages
Terraforming allows you to increase the fields on an existing planet, allowing you to continually progress to larger levels of buildings, and retain control of whichever planet slot your world is in.
Terraforming is almost never won through the daily lottery, and will therefore usually need to be bought with credits.
Alternatives
Other than terraforming, the only way to get more fields is by repeatedly building Gaia class colony ships, launching them on colonize missions, and abandoning the colonies if they do not have enough fields; this can take a lot of resources, especially crystal. You will also need to abandon a planet you already own, unless you have empty planet slots already. Building all those Gaias, and launching them off also takes time.
Warning
The Terraform button works on whichever planet you currently have selected. It is best to be on the home or building page, so you can be absolutely certain that you have selected the correct planet to terraform.