parent.js

// Packages, Components
import React, { Component } from "react";
import SearchField from "../components/SearchField";

class Search extends Component {
  constructor(props) {
    super(props);
    this.state = {
      keyword: ""
    };
  }

  handleKeyword = keyword => {
    this.setState({
      keyword
    });
  };

  handleFetch = () => {
    // Your fetch code here, access keyword with this.state.keyword
    // You can also pass it in as a parameter but its up to you
  };

  render() {
    return (
      <div>
        <SearchField
          keyword={this.state.keyword}
          handleKeyword={this.handleKeyword}
          handleFetch={this.handleFetch}
        />
      </div>
    );
  }
}

export default Search;