Luxembourg is a tiny country, and it's possible to get essentially anywhere in less than an hour. Bus services are excellent within Luxembourg City, and most routes pass through the central bus station, making it easy to get to most places. A standard ticket is €2, while a day pass is €4. The buses also travel out to villages like Junglinster, Mersch, Trier, and Wasserbillig.
Bus tickets are valid on the train network, which is relatively comprehensive throughout the country and connects to destinations in Germany and Belgium. Renting a car in Luxembourg is also an option as local drivers are polite and the road system is well-developed. Parking can be difficult to find on weekends in Luxembourg City.