The University Campus is located about 5km outside the city center of Limerick. Therefore, most students choose to live on campus or in the surrounding areas, such as Castletroy or Milford Grange. If you would like to live in one of the many student villages on campus, you can find useful information on the following UL website: https://studentliving.ul.ie/index.jsp?p=116&n=129
Prices vary considerably (ca. 4500€ - 8500€ for the academic year), depending on village location and the number of students that share an apartment. Student accommodation rates for 2018/19 can be viewed here: https://studentliving.ul.ie/index.jsp?p=116&n=124
There are also off-campus student accommodations (https://studentliving.ul.ie/index.jsp?p=116&n=141), approx. a 20 minute walk from campus, such as Troy Village, Groody Park, Courtyard or Brookfield, which is located a little further from college, but offers a bus service to and from campus.
Furthermore, students have the option of living in private accommodations, such as shared flats and houses. This is the option I chose as it tends to be cheaper (ca. 300€ a month) than the student accommodation. You can search on your own on websites like daft.ie or rent.ie or, in my case, the university sent out an email to the international students with a list of possible housing options in spring, so maybe be on the lookout for that.