The easiest way is to use react-native-paper package with their text input:

import * as React from 'react';
import { TextInput } from 'react-native-paper';

const MyComponent = () => {
  const [text, setText] = React.useState('');

  return (
    <TextInput
      label="Email"
      value={text}
      onChangeText={text => setText(text)}
    />
  );
};

export default MyComponent;

Result:

Here is what I use without any library, working example and if you want to add animation to the fields working example with animation

import React, { Component } from 'react';
import {
  View,
  StatusBar,
  TextInput,
  Text,
} from 'react-native';

class FloatingLabelInput extends Component {
  state = {
    isFocused: false,
  };

  handleFocus = () => this.setState({ isFocused: true });
  handleBlur = () => this.setState({ isFocused: false });

  render() {
    const { label, ...props } = this.props;
    const { isFocused } = this.state;
    const labelStyle = {
      position: 'absolute',
      left: 0,
      top: !isFocused ? 18 : 0,
      fontSize: !isFocused ? 20 : 14,
      color: !isFocused ? '#aaa' : '#000',
    };
    return (
      <View style={{ paddingTop: 18 }}>
        <Text style={labelStyle}>
          {label}
        </Text>
        <TextInput
          {...props}
          style={{ height: 26, fontSize: 20, color: '#000', borderBottomWidth: 1, borderBottomColor: '#555' }}
          onFocus={this.handleFocus}
          onBlur={this.handleBlur}
          blurOnSubmit
        />
      </View>
    );
  }
}


export default class App extends Component {
  state = {
    value: '',
  };

  handleTextChange = (newText) => this.setState({ value: newText });

  render() {
    return (
      <View style={{ flex: 1, padding: 30, backgroundColor: '#f5fcff' }}>
        <StatusBar hidden />
        <FloatingLabelInput
          label="Email"
          value={this.state.value}
          onChangeText={this.handleTextChange}
        />
      </View>
    );
  }
}