A field is an area of study, usually designated by time and place, and sometimes also by some other kind of theme. So "Early Medieval Europe" might be a field, or "Women in Silla Korea."

Within a field, how you choose to study is often called an approach. Some common ones you'll hear about might include social history, political history, economic history, and others. So if you're studying early medieval Europe with a social history approach, you might write about something like how old people were when they got married and how they chose their spouses, whereas if you were writing about that field with a political history approach, you might write about Charlemagne and how he tried to create a unified empire. A technique is maybe a little more specific than an approach, but not that different.