Your first port of call should be SOLO which covers both print and online newspapers as well as microforms.
It can be really difficult to find newspapers in SOLO, mainly because they tend to have common names. For instance, a search on the Times returns over 43,000 items.
Here is an example how to best locate The Daily Mail in SOLO, using Advanced Search:
It helps to narrow down your searches by using the drop down menus.
Newspapers are generally considered to be journals and so it can be sensible to choose “journals” from the drop down menu. However, due to the way in which we receive journals, some are listed as databases. The safest option is to start by choosing "journals". If you don’t find what you want try "databases".
For the second drop down menu, by far the best option is “starts with”. This will drastically reduce the number of results. Clearly you need to make sure that you do know the first word of the journal. For example, we may colloquially talk about The Mirror but to search for it here, you need to use its full name “The Daily Mirror”.
Finally for the third option choose “in title”.