The short answer is it required a lot of manual labour no matter what, but different aids and a clever research question could make it manageable. As newspapers have existed for centuries in countries all over the world it’s extremely difficult to give a specific answer. So this is mostly some broad trends.

In most countries most or all published newspapers are kept in libraries or archives, often in a centralised state library. Here the papers are kept on micro film rolls. It takes time to go through a month let alone a year of a specific newspaper. In most studies you would need to look at several different newspapers to balance the political biases of the papers further expanding the amount work needed.

When reading a lot of historical newspapers from a specific area and period you learn that they a structured and edited in a systematic way. Local, national, international and business news is usually ordered in a specific way. Depending on the research question you would often only need to look at 1-4 pages to see if there is any relevant pieces. Furthermore, depending on the time and place some aids can be available. Newspaper yearbooks, registers and indexes are very helpful when available. Newspaper cutting was a big business from the late nineteenth century until the digital age. Akin to email newsletters politicians, state agencies and especially big businesses would receive a daily bulletin of newspaper articles relevant to their field/area. It saved the decision makers the time of sifting through several newspapers each morning. When these press cuttings or scrap books are conserved in state or business archives it saves the researcher a lot of time as well although she/he must remain critical of any bias.

To cut down the time needed the research question can be toned to make it more manageable. Years ago I made a study of political parades. As they occurred on specific dates I knew beforehand I only needed to look at papers for some days before and after the events. When I tried to expand the study to random political manifestations through the year the task grew immensely.

When no other aids were available only the brute force method of scrolling meter after meter of microfilm remained. If you were a professor or someone with a research grant that usually meant putting a lot of research assistants to work. For a junior researcher logging the hours at the archive was the only option.