Let's start with the honest statement that you are always assuming additional risk of death or injury if you choose to fly! As home-built/ultralight aircraft go, most gyro pilots consider their aircraft to be very safe and even superior, in many ways, to conventional fixed-wing aircraft. That said, many conventional pilots have a negative impression of gyroplane safety. The simple fact is, most gyroplane fatalities and serious accidents happen to people who try to teach themselves to fly. This is particularly true of experienced fixed-wing pilots who are sure they can easily handle something as "simple" as a gyro! In fact, they are simple to fly but they are unique aircraft and training is essential. The basic principles of safe gyro flying are really quite simple:

Get dual training from a qualified instructor. See the question on learning to fly for the reasons!

Inspect your machine carefully prior to every flight. Gyroplanes are rugged little machines and it is very easy to inspect everything! Accidents or incidents due to component failures are not accidental at all. Invariably, the problem is that the pilot failed no notice stressed or worn parts.

Know and respect your personal limits as a pilot as well as the limits of your aircraft. Each time you fly, you have to evaluate the flying site, the conditions, and your own state of mind. Your capabilities as a pilot will increase with experience, but it is a gradual process that should not be rushed. If you are conservative in taking on new challenges and "expanding your envelope", you will do just fine.