Access to journals is a great deal easier if you are at university, or if you graduated from a university which provides alumni access to journal databases (the latter often seem to be higher-ranked, well-off universities such as Ivies and equivalent in the US, and Russell Group in the UK. Which, yeah, isn't that fair. Jstor's list of universities giving alumni access - some of these also provide access to additional databases. You can also get free access to 6 articles per month on JStor without a university connection.)

There are other record sets which are available to members of the public, often for a fee. For example censuses and passenger lists, as well as birth, marriage and death records, are available on genealogy websites such as FindMyPast and Ancestry - and other countries have their equivalents.
Online newspaper archives can also be accessed by the public, including independent researchers, for a fee. In the UK these include the British Newspaper Archive, which is part of FindMyPast, and newspapers.com.

Some types of primary source information can be found online for free. Some American newspapers make their articles available going back decades.
Many obscure out-of-copyright books, including volumes over 100 years old, can be found on archive.org. The Hathi Trust is a repository for large volumes of archival documents from several countries. I wouldn't even like to start summarising what's in there, as there is now so much, but in the last couple of weeks, I used it to look at some medieval and early modern English legislation and proclamations, which could be read in neatly scanned pages from books compiled in the Georgian to Edwardian periods. (Another user on here told me that was now the place to find it.)

Letters may be found in published collected volumes, especially if they are from famous literary or historical figures - but for more obscure ones, the researcher may have to visit an archive (e.g. at a university or museum).

The general bibliography for Ferguson's Empire mentions a thematic sourcebook, another type of publication which can also be very useful - a collection of primary sources of various types; where relevant, these may be from more than one country. (Harlow & Carter, Imperialism and Orientalism: A Documentary Sourcebook.) Sourcebooks may also provide non-written material such as caricatures, art or maps. For thoroughly-studied countries, volumes of statistics, such as British Historical Statistics (that one still, frustratingly, not in an electronic form) may be available.

As to what percentage of whole books people read, as opposed to chapters and consulting from indices, that seems to vary a fair bit, depending on personal preference and reading speed. (I've noticed some differences about people's take on this online depending on nationality and type of university, and would be interested in hearing what those currently in postgrad or academia say.)

Where relevant, and where there are funds available, there may also be travel - to conferences, or to look around a location being researched. Conferences can also be another way for people to hear about the latest research - although as agendas are often available online, some idea of what goes on at them is still available without attending, and papers may be put online later.