As a foreigner you must declare yourself to the city hall within 10 days of arrival (or so). The foreigner arrival page tells you what you need to register.
NB: as of 2015 many city hall tasks have been outsourced to towns on the outskirts of Liège (id cards and arrivals are still in the main building near Decathlon). Check the city web site and the submenu for your request – they give opening hours and addresses.
Once you have a definitive address (or anytime you change) you have to go with a copy of your rental contract and update/obtain your ID card. They give you a temporary form and within 2 weeks or so a policeman comes around to check you actually live where you say you do. Sometimes on Sundays, sometimes they don’t come at all, and sometimes they just leave a note saying they came by and everything is fine. 2 further weeks after the check your card should be at the city hall and you can go get it (normally they do not notify you).
The different city halls are listed with a phone number on the City of Liege web site.
Opening hours for the central hall are:
Mon-Thu: 8h30 à 12h30 et de 14h à 16h
Friday: 8h30 à 12h30
In the central city hall Potiérue 5 there is at least one person who speaks Turkish and several who speak English.
Note that for routine official documents there are many you can order online (this could be reserved for Belgians, have not checked). You pay by bank transfer with a code they give you to identify your request, then you go pick them up or have them mailed to you.