When a company decides to issue more shares in a secondary offering, how is the price determined?

At what price should they be sold? And who determines the price?

It's very similar to an IPO. The market (meaning the people that buy the shares) determines the price. There will typically be an underwriter in the middle that will agree to buy the shares for a specific price (based on what they think the market will pay for them), then facilitate the sale of those shares on the open market, hoping to make a profit overall. The market may be willing to pay more or less than the existing shares, depending on what the company plans to do with the proceeds.