Even if you can't read ancient languages, you can use primary sources for ancient history. Sometimes it may be better to use secondary sources because ancient historians were not always as reliable as we might wish. The Greek Herodotus is credited with inventing history, but his writing was filled with legends and even myths. Thucydides called him the "father of lies."
Ancient Monuments
You have an advantage over many people interested in ancient history if you can read the ancient languages like cuneiform and hieroglyphs. Primary sources include funeral monuments, stela and the inscriptions on statues regularly exhibited at museums.
Other Ancient Written Sources
Most of us must rely on the printed page. Since the works of many ancient Greco-Roman writers survive, we have a large body of primary material on the Greeks and Romans. Some of this is history proper, but don't discount the literary. Read it for insight into the customs, lifestyles and beliefs of the ancient people and their opinion of other peoples with whom they came into contact.
Ancient Secondary Sources
Tacitus says his predecessors flattered the emperors whose histories they wrote. Sometimes it's hard to see what's going on around you while you're living it. A slightly later secondary source (actually, often referred to as primary) provides a much better look at events than a history written centuries after almost everyone has forgotten the events.
Tacitus Books
Modern Secondary Sources
While those who lived at or near the time of ancient events knew much about what happened that we'll never even guess at, modern authors can string together archaeological, epigraphical, literary and historical information from the past to present a well-rounded picture of ancient history.
Scullard Books