Birds may not seem like ideal traveling companions, but there will be occasions when you need to move your bird from one place to another whether it be to actually move residences or to actually take a trip with your bird.
Regardless of your own feelings about traveling, remember that birds are more comfortable in familiar surroundings and may become quite stressed if moved about needlessly. Depending on the nature of your travel, you might consider bringing your regular bird cage along to give your pet bird a familiar resting place. Also pack your usual bird food. You might not be able to find the right kind at your destination.
Some larger birds are happy to be moved about in small dog carriers, but there are many carriers specialized designed for traveling with birds. Introduce your carrier to your bird well in advance of the trip.
Traveling by car isn't so difficult as you can control the environment and circumstances of the trip. A small bird cage can be an ideal carrier while in a car. Keep hard, swinging bird toys out though. They can swing around in a moving vehicle and be a hazard for your bird.
Longer trips that involve air travel can be more problematic. Do your research. Don't just show up at the airport with a bird. Many airlines will allow you to take your bird with you to your seat as a carry-on rather than stowing it in the cargo hold. This may not be an option for larger birds like macaws. Be prepared to provide a health certificate from the vet's before your board the plane.
If you are leaving the United States, start planning at least a month in advance. Most pet birds are exempt from some quarantine procedures if they are US-born. Check the regulations at your destination and get those regulations in writing so you can ensure you comply with them.
It can be quite an ordeal to travel with a bird. You might want to consider finding a caregiver to take care of your pet at home while you are away.