When doing historical research, you may find that you want to work with original documents. There are many reasons for this. It represents the most effective way of doing high quality research, and the only way that avoids being derivative of others. It is necessary for anything academic. It also gives you a much more direct insight into the time you're playing around with. So, how do you do it?
First, find your archival source. Many have transcripts online these days, from census records to even quite obscure sources such as medieval fight books and official charters. Project Gutemburg has a lot, while general sites on areas of expertise will often be able to point you in the direction of more. Forums can be your friend here, as people will often post links or upload copies of out of copyright documents.
If it isn't online, you may need to visit in the flesh. That means finding where to go. In the UK, the National Archives keep records of many public archives throughout the country, along with their contents. General books on the topic may contain references to key archival sources in their bibliographies, along with their locations. A little travelling can bring you face to page with anything from fourteenth century minster charter collections to an original Domesday Book. Generally, they get the cushions in the archives. You don't. Getting access is mostly a question of asking, then possibly paying a fee for access to the library.
Consider whether you really need or want the original. If you're doing serious academic research, then yes, it's a good idea to check for charters people might have missed, or phrases they might have mis-translated. Otherwise, you might find that books of collected primary sources might be just as good, if not better. They still give you access to words from the past, but suddenly, you might not need to learn Latin, or learn to read seven hundred year old handwriting. Plus, sources from several places can be collected together. Generally, there are series for major sources of archival material, such as the Admiralty, the royal pipe rolls, archiepiscopal papers, etc, as well as one off volumes for individual institutions, often produced by regional historical societies. Large university libraries will usually have many of them, or will at least know where they can be found.
Finally, keep your objectives in mind when reading them. It can be fun to go through aimlessly, but the danger is that the wealth of material can make it easy to be overwhelmed. Ask questions of the archival material instead. Literally write out a set of questions, and search for sources that could answer them.
Remember to think about why the sources were written. We get a lot of material from old trials, for example, because they tend to be some of the few records ordinary people show up in for some medieval towns. The danger is that we then think that medieval people were a bunch of criminals. Think about who was writing it and why. Then think of all the uses you can put it to that have nothing to do with what they intended. Charters, for example, are sometimes more interesting for who was there as a witness than for their content, because they help to place important people in particular places at particular times.