Clicking sound when turning wheel right?

I'll assume you have a front-wheel drive. These have CV or Constant Velocity joints in the drive arms - necessary because the drive shafts need to bend as you steer. They are like a Universal Joint except the architecture is designed to literally transmit a constant velocity through the joint. (A plain Universal Joint will cause a slight increase and decrease of speed on the other side of the joint as the pivots move during rotation)

The CV joint needs to be packed with grease, and then the joint is covered in a rubber boot. These rubber boots unfortunately can split and then the grease can fall out; also dirt can get in. The lack of grease along with the dirt will damage the joint, leading at first to a ticking sound when the joint is bent through a large angle. As the damage gets worse, the tick will happen at smaller and smaller angles. If the tick is only on one side, you've probably got a split only in the boot that's on the inside of the turn (ie the right-hand boot for this question)

If the damage is very minor you could get away with cleaning, repacking and replacing the boot, but in general you'll need to get the shaft or joint replaced - not necessarily new because they can be reconditioned quite easily.