If traveling by car, there are a few measures you can take to assure a safe and enjoyable drive. The safest place for your pet to travel is in its crate. Sitting on your lap is probably the most unsafe place for your pet to travel...for both you and your pet. If your pet is not used to long distance traveling, do a few quick test runs before your actual trip, gradually increasing the length of the car ride. If your pet is not used to being crated, leave the crate out well before your trip, with the door open so your pet can go in and out freely. Alternatively, there are specially designed seat belts and other equipment to keep your pet safe and secure in the car. If you know your pet gets car sick or overly anxious on trips, your veterinarian will be able to prescribe medications for your pet to relax their tummies and minds. Also, withhold food from your pet several hours before traveling to help prevent any upset tummies (don't withhold food from young puppies and kittens or other pets that cannot physically tolerate fasting).
If traveling by plane, make sure your airline of choice will also transport your pet. Each airline will have specific requirements for flying your pet, including specific climate conditions, crate types, and even the size of your pet. If it is too hot or too cold, most airlines will not fly your pets. Check with your specific airline for their requirements.
If traveling out of state or out of country, your pet may need a health certificate, certain vaccinations, or even to be quarantined on arrival. Check the laws of your destination (or ask your veterinarian to help you find this information) to make sure you have the appropriate health papers and records for your pet.
Check hotels and other lodging prior to your vacation to make sure they are pet-friendly and that you know the details of their pet policies.
The most important thing to remember about traveling with your pet is to plan ahead.