Get a tapejara and a tribesmember. One of you ride on the back of the saddle, the other drive. The person on the back should have either a crossbow and flame arrows or a flamethrower, if you're feeling daring. Fly near one and eat a rare flower. The phoenix will chase you, so you can fly away and the person on the back shoots the phoenix. Make sure you have ghille and cactus broth, because they only spawn in heat waves. If you are on a server where you can transfer dinos, you can build a metal box with an open side on the back of a quetzal, let the phoenix fly in, and wall up the opening. Proceed to light it up...literally. If you follow the phoenix during a heat wave, when it deepens know that next heatwave it will spawn in the same place. Build a large platform out of any material under where the phoenix will spawn. Wait for a heatwave, then quickly bola the phoenix and box it in. You can either build a big box and go in with it, or make a window you can shoot it through. Good luck!
You can get it to spawn next to your base because of the following: It always respawns at it's last location, so if the heatwave ends while you are following it you will know where it is for the next heatwave. It also chases you when you eat flowers... hint hint
Find a phenix during a heatwave and follow it until it ends. The phenix will turn into ashes and land on the ground but will spawn right back at the same exact spot during the next heatwave. Build a trap 6 blocks high so I can't glitch out and you have yourself a trapped phenix to tame:)