I bought at Garmin Nuvi 1300 GPS for my daughter for Christmas. She just tried to use it for the first time yesterday and it doesn't fit the cigarette lighter. What can we do now???

That plug contains a voltage regulator to change 12V to 5V. DO NOT connect the wires directly to 12V.

If you find any problem in setting up the Garmin device just download Garmin express its an easy to use computer application that helps in easily setting up, registering and managing your garmin device. it also moderates and watches the work of other garmin devices on your computer.
visit this site for more info: https://i-garmin.com/garmin-express/

My gps adapter dont fit in my mazda 3 cigarette lighter, how can i get it to fit?

It's strange if the plug doesn't fit the cigarette lighter socket. They can be a tight fit so if you find it a little big for the socket try putting pressure on it to push it in. If it absolutely won't fit you can buy cigarette lighter plugs in car accessory shops. If you can get one that does fit you can cut the one that's on the lead off and fit the new one.

If you cannot get any plug to fit you can get the lead wired permanently into the car. Any garage would be able to do it for you.