It really depends on the culture, but I'll look at the western culture overall. Surprisingly, they still used rings! This is true even as far back as Ancient Egypt. Metals were used as a currency and men would have a metal ring to place on the woman as a way of giving his wealth for her commitment to him.

In the Roman period women were given two rings, one made of iron and one made of gold. Gold was to be worn outside of the home while iron was worn for home duties so the gold wouldn't be ruined.

Varieties of metals such as iron have been used throughout the middle ages, Renaissance, and other periods of time. It was only until the famous DeBeers campaign "A diamond is forever" that it became the defacto choice of engagement. I think the idea that engagement rings didn't exist until DeBeers is an exaggeration that they started the idea of engagement rings. Rather, they only altered what they thought people should use as a ring.

See also betrothal, the Jewish tradition of announcing intent to marry. Different custom that has existed since the BCE period. It was more of a formal question, but even in Chayei Sarah 24 is a ring used.

Sources:

• The Little Giant Encyclopedia of Wedding Etiquette
• The Roman Wedding Ring

The previous answers from the FAQ may also prove illuminating.