const componentWrapper = mount(<MyComponent />);
componentWrapper.find("input").simulate('change', { target: { value: "valueToSet" }});
When attempting to simulate setting a value to a field, React will need a pair of value and onChange methods to be able to register the changes (controlled).
e.g.
<textarea value={this.state.myValue} onChange={(e) => { this.setState({myValue: e.target.value}); }} />