A lot of Luxembourg City is either one-way or bus lanes or both. It is worth looking carefully at a map and understanding both the road layout and the very three dimensional character of the town. Also watch out for the new tram system - if your map is not new it may not be on there, and if your sat-nav isn't updated you may run across it unexpectedly. If you are not careful you will find yourself going up or down a steep hill or across a bridge that you don't want to cross.
Lots of traffic lights, often with different filters for different lanes.
Free street parking is very rare, all the parking signs are in French or Lëtzebuergesch and will have hour and day restrictions. Paying is almost always at a horodateur and some have more than one language on them.
Much easier, but no less expensive, is parking in one of the many underground garages. They are normally pay on foot, pay at the end, and the machines are almost all multilingual.
Easiest is to park out of town at one of the chains out in the countryside. They're reasonable value for money (you pay a lot for stars) and often have inexpensive or free parking. I've had good success with the Doubletree - lots of free parking but by no means free breakfast (tasty but expensive even for Honors), the bus stops just down the hill and goes to the centre and Kirchberg; the Mercure on the golf course (good but expensive breakfast sometimes on a deal for Accor, tons of free parking, nice walks in the woods or on the golf course, zero public transport nearby), or at the various Ibis variants scattered around (less expensive and much less extensive breakfasts, good deals for Accor, cookie cutter rooms, some offer parking, some charge).