If you work in the private sector, your employer automatically deducts tax. If you meet certain criteria, Luxembourg will ask you to file a tax return, but this is not necessary.
If you have paid too much, you can claim back the difference in the overpaid amount with a so-called »décompte annuel". Taking into account various recognized reliefs, you can do the calculation yourself, or you can contact an accountant for professional help, e.g. to Sladjana Todorović, where members will also get a 20 % discount.
Remember - a professional calculation usually costs less than €100, but you can get a lot more back.
You can get Siljanine's contacts and the discount form at this link.