They can issue shares of stock, they can borrow from the bank, or they can borrow from investors by issuing bonds. Corporate bonds come in dozens of varieties. Many corporate bonds feature a call provision that allows the issuing company to pay back the principal to bond holders before maturity. Other corporate bonds are known as convertibles because they carry a provision that the bond can be converted into shares of common stock under certain circumstances. Convertible bonds can be more attractive that bonds with no conversion provision, depending on the price of the underlying stock.
Most corporate bonds are fixed-rate bonds.
The interest rate the corporation pays is fixed until maturity and will never change. Some corporate bonds use floating rates to determine the exact interest rate paid to bond holders. The interest rate paid on these bonds actually changes, depending on some index, such as short-term Treasury bills or money markets. Other corporate bonds, called zero-coupons, make no regular interest payments at all. Yes, but it's not a trick.