Take your car to a mechanic and get it looked at. Make sure that all belts and hoses are in good condition, and all fluids are topped up. Make sure you know the rate at which your engine burns oil, so you know how often to check it, and carry spare oil with you. Make sure your tires have plenty of tread and are properly inflated, and have no sidewall damage, and monitor the tire pressure regularly. Ideally, carry a spare tire and jack and wrench, but a lot of newer cars don't come with these anymore, which is lamentable.
Other than that, you don't have to do very much, as long as the vehicle is in good shape.
Last year I took my then ten-year-old Honda over 5,000 km (~3100 mi.) from Saskatchewan to see the eclipse and visit the US west coast, and other than two stone chips on the windshield, I had no problems. This year I'm taking it almost 6,000 km (~3725 mi.) to Texas via Kansas City, and back via Santa Fe, Denver and Deadwood, and I'm not terribly worried. There is a chance I could have a failure, but that is possible with a newer car, too. (My car has just over 192,000 km (~119,300 mi.) on it.)
Drive safely - know your route in advance if possible. Be well rested, take adequate breaks for food, drink and bathroom relief (and resting your eyes and body), and enjoy the trip. Make sure you have a fully-charged phone with you in case you have trouble, and carry lots of water, especially in the summer, in case you get thirsty in an isolated area.