Was America involved in wars during the 80's and 90's?

Yes, but they were mostly small or minor conflicts that often get overlooked in schoolbooks.

Granada, Panama, The Gulf War (if you don't hear about this one in a textbook, your school is a quack school for picking a crappy text), former Yugoslavia, Somalia, Beirut, and Nicaragua to name a few.

The Gulf War, Granada, and Somalia are the most well-known of the three. The Gulf War for obvious reasons, Granada because in spite of the outright dominance that the US exhibited against the Cubans, results from the battlefield showed that the branches of the military needed better communications between each other. Somalia is infamous for the Black Hawk Down incident.

Technically, many of these are actually 'Police actions," not wars, at least officially.

Us Wars In The 80s

There weren't any large wars but there was Operation Urgent Fury in Grenada, Operation Just Cause in Panama, Operation Desert Shield/Storm in Iraq, some involvement in Somalia then kind of the Kosovo war.

During times of peace the military trains for war.

Yes there were wars. The most notable being the Gulf War. Iraq invaded Kuwait and the UN formed a coalition of countries led by the United States to stop Iraq. Almost all of the major combat was done by the US who committed 575,000 - 697,000 troops. Total coalition strength was close to a million troops. Iraq's invasion was stopped, sanctions were imposed, and their military suffered enormous losses at the hands of superior coalition forces. The coalition lost 397 troops and the Iraqi military is estimated to have lost 20,000–35,000. Not to mention heavy losses of military equipment. The Iraqis were no match for the US led coalition.

http://en.wikipedia.org/wiki/Gulf_War

We were involved in several conflicts.. Not sure if they'd be considered wars.. Except the first Desert Storm, of course.

Off the top of my head, there's Panama (Just Cause), Grenada, Haiti, Somalia, Iraq (Desert Storm), Bosnia and Serbia.