There were a total of five generations of the Tercel. The first generation started in Japan in 1978. The Tercel would not be sold in the United States until 1980. The car marked a big change for the Toyota brand, as it was the first front wheel drive car they had ever produced. It's original name was the Corolla Tercel. At the time, Corolla was a name that had become synonymous with quality and a long lifespan. Those first models were sold with a 1.5 liter I4 engine that made about 60 horsepower.
The second generation Tercel was sold from 1983 through 1986. The Tercel was sold in 4 different body types: 3 door hatchback, 4 door sedan, 5 door hatchback, and 5 door station wagon. If I remember correctly the 3 door hatchback was the popular choice in the United States. The station wagon version could be purchased with 4 wheel drive, which could be switched to 2 wheel drive and back again without having to stop the car. The Tercel station wagon was not meant to be driven in 4 wheel drive full-time because it would destroy the drivetrain, so it was really more of a emergency system for bad road conditions.
The third generation Tercel was sold from 1987 until 1990. It added some luxury features, but it was still priced at a point that made it an economy car. To appease the entry level buyer, Toyota introduced the Tercel EZ in 1988. It was basically a Tercel with fewer features and a lower price.
The fourth generation Tercel was sold from 1991 until 1994. The 5 door wagon configuration was dropped, with the trims in the U.S. models being the base, DX coupe, DX sedan, and the LE sedan.
The fifth generation would be the final one for the Tercel. It lasted from 1995 until 1999. New safety features like dual airbags were added, along with a lot of other features that had previously only been optional equipment. The CE classic trim was the only one offered in the United States by 1997. The Tercel was dropped in order to make room for the totally new Toyota Echo, which was clearly an effort by Toyota to make an eco-friendly gasoline powered car.
The Toyota Tercel was such a popular car for so long, there should be no problem finding a decent used Tercel. Instead of spending weeks or months searching the local used car market, I suggest just browsing on over to eBay. It's way easier, and I really am that lazy.