Historians, as a budding History major (because I love it), I have quite the embarrassing dilemma.
I have extreme anxiety when reading and analyzing primary sources.
When I read primary sources, I often have no insights popping into my head. I try my best to think of any significance to the reading, but most times, I just can't do it.
Whenever I go to discussion sections in my university, I always hear these deep comments from my fellow classmates and it always makes me wonder why I could not notice that before.
I have read multiple guides, and have received some handouts on how to read primary sources from my professors. They help a bit, but I can't help but face the fact that even if I answer all the questions that I'm supposed to ask, I still can't make a good conclusion or analysis.
So historians, any advice for me?
Not a historian per-se, but I do work with documents and I think the answer to your question is going to be very similar across all the social sciences.
I would suggest that maybe you are going about the process backwards. In independent research you want to have a question to answer and pick your primary sources to best answer that question. Different sources are going to have different strengths.
For instance, baptismal records from a Spanish colonial church in northern Mexico are going to be a great source for figuring out changes in population size as well as looking at say intermarriage between different ethnic groups brought together at the church. Those sorts of demographic questions suit the source much better than say asking questions about political intrigues determining who ended up as the Viceroy of New Spain. If that was the research question I wanted to answer I probably wouldn't use the baptismal records, or at least I wouldn't start with them.
Of course, when you are in a class you don't start with the research question - you are assigned the primary source and have to draw something from it. That isn't the ideal situation, but you can apply the same approach in reverse. Ask yourself what sorts of research questions you could ask that would lead you to using that source?
As another approach, I would say there are generally three kinds of questions historians (and social scientists generally) are interested in answering.
First, how do societies function or stay together? E.g., why don't people chop off the king's head?
Second, why do societies break apart or how do they not function? E.g., why do people chop off the king's head?
Third, why and how do societies change over time? E.g. did they replace the monarchy with a parliament or did they install a new monarch? Why?
Basically, start with a question (even one as general as the three I outlined above) and ask what the source you are looking at is best suited to addressing. Can the source tell you more about how the society is changing, or can it tell you more about how the society functions (or doesn't function)?
Also, go talk to your professor in office hours. Depends on the professor, but many are going to be really excited that anyone bothered to show up for office hours in the first place and even more excited that their student is interested in working on being a better historian. You could even ask them if there is a source you could read that both of you could go over and analyze together just one on one.
Edit: For grammar and typos.
I have two suggestions that helped me in undergrad:
Think critically about the facts and viewpoint being presented. Ask yourself:
What is there author's motivation for presenting this information? Everything you read has some personal motivation behind it, understanding why the author is writing will help you understand how much to trust the facts they present, compare them to competing points of view, and inform when you need to find more sources.
Why are you reading this source? Frequently your answer will be "my professor choose it", so you need to understand why your professor chooses the particular source. Is it the only one available? If not, do other sources express opposing points of view? If it's the only source, why is that - destruction of other sources, lack of interest from contemporary writers, lack of literacy in other segments of the population?
Think about this source as the basis for an argument. What can you argue in favor of or against with this source? Are there specific facts that support what you've read elsewhere?
Read more. Reading historical analyses will let you see how historians break down primary sources. Reading primary sources will let you practice those skills. Doing both will also give you a wider contextual view to analyze from - you'll be able to make connections from what you've read to related works, and you'll see how arguments you've read fit into larger historical narratives.
Being a good historian requires amassing a range of intellectual skills and knowledge, this is a normal part of undergrad. Don't worry if you don't feel as insightful as your peers right now, your interest and desire to improve will serve you well!