Books written during (or shortly after) the time period can often be great examples of primary sources, especially when it comes to ancient history.
Because these books are so old, they are often freely available on the internet.
Google is becoming a really great place to find primary sources. The key to finding them is how you construct your search.
You'll always want to add a keyword to the end of your search that will help you find primary sources specifically. Examples of those terms are: "primary sources," documents, archives, correspondence, images, texts, writings, works, etc.
A few example searches:
The battle of thermopylae "primary sources"
The Trojan War documents
You can also add site:.edu to the end of any search in order to make sure you only bring back .edu sites. That can help with weeding out potentially unreliable sites.
The battle of thermopylae documents site:.edu