This article doesn't say, but vertical farms almost always grow hydroponically, using sterilized inert media (like coir) or inherently sterile inert media (like rockwool). The water and fertilizer are delivered together by drip irrigation. Some farms may instead use no medium at all, like in NFT or DWC. With precise control over the plant nutrition, this can achieve higher yields per square foot than soil, making optimal use of the expensive indoor space. (I think grains are particularly unsuitable crops though, per my other comments here.)

In theory it's possible to run completely free of insects, with cleanroom-like precautions, and I think some facilities do. I think it's more common to live with some level of insect pests though, since it's so hard to avoid introductions and so destructive when they occur--with no natural predators, they can multiply far faster than in nature. That implies some level of pesticides, deliberately introduced predatory insects (which are particularly effective indoors, since they can't fly away), etc.