What is the value of an 1889 American eagle silver dollar coin?

It's actually a real silver dollar called a Morgan dollar after its designer George Morgan.

The "eagle" coins weren't issued until the 1980s and are bullion coins sold as investments and not for spending, but Morgan dollars were struck for use in ordinary commerce back in the days when silver was worth far less than it is now. You could get them at a bank and spend them like any other coin.