Ok, so I'm sorry but most of these answers are incomplete or have some minor bug in them. The very complete answer from @austyn-mahoney is correct and the source for this answer, but it's complicated and you probably just want to style a switch. 'Styling' controls across different versions of Android is an epic pain in the ass. After pulling my hair out for days on a project with very tight design constraints I finally broke down and wrote a test app and then really dug in and tested the various solutions out there for styling switches and check-boxes, since when a design has one it frequently has the other. Here's what I found...

First: You can't actually style either of them, but you can apply a theme to all of them, or just one of them.

Second: You can do it all from XML and you don't need a second values-v21/styles.xml.

Third: when it comes to switches you have two basic choices if you want to support older versions of Android (like I'm sure you do)...

1. You can use a SwitchCompat and you will be able to make it look the same across platforms.
2. You can use a Switch and you will be able to theme it with the rest of your theme, or just that particular switch and on older versions of Android you'll just see an unstyled older square switch.

Ok now for the simple reference code. Again if you create a simple Hello World! and drop this code in you can play to your hearts content. All of that is boiler plate here so I'm just going to include the XML for the activity and the style...

activity_main.xml...

<?xml version="1.0" encoding="utf-8"?>

<RelativeLayout

    android:layout_width="match_parent"

    android:layout_height="wrap_content"

    android:paddingBottom="@dimen/activity_vertical_margin"

    android:paddingLeft="@dimen/activity_horizontal_margin"

    android:paddingRight="@dimen/activity_horizontal_margin"

    android:paddingTop="@dimen/activity_vertical_margin"

    tools:context="com.kunai.switchtest.MainActivity">

    <TextView

        android:layout_width="wrap_content"

        android:layout_height="wrap_content"

        android:text="'Styled' SwitchCompat" />

    <android.support.v7.widget.SwitchCompat

        android:id="@+id/switch_item"

        android:layout_width="wrap_content"

        android:layout_height="46dp"

        android:layout_alignParentEnd="true"

        android:layout_marginEnd="16dp"

        android:checked="true"

        android:longClickable="false"

        android:textOff="OFF"

        android:textOn="ON"

        app:switchTextAppearance="@style/BrandedSwitch.text"

        app:theme="@style/BrandedSwitch.control"

        app:showText="true" />

</RelativeLayout>

<RelativeLayout

    android:layout_width="match_parent"

    android:layout_height="wrap_content"

    android:paddingBottom="@dimen/activity_vertical_margin"

    android:paddingLeft="@dimen/activity_horizontal_margin"

    android:paddingRight="@dimen/activity_horizontal_margin"

    android:paddingTop="@dimen/activity_vertical_margin"

    tools:context="com.kunai.switchtest.MainActivity">

    <TextView

        android:layout_width="wrap_content"

        android:layout_height="wrap_content"

        android:text="Themed SwitchCompat" />

    <android.support.v7.widget.SwitchCompat

        android:id="@+id/switch_item2"

        android:layout_width="wrap_content"

        android:layout_height="46dp"

        android:layout_alignParentEnd="true"

        android:layout_marginEnd="16dp"

        android:checked="true"

        android:longClickable="false" />

</RelativeLayout>

<RelativeLayout

    android:layout_width="match_parent"

    android:layout_height="wrap_content"

    android:paddingBottom="@dimen/activity_vertical_margin"

    android:paddingLeft="@dimen/activity_horizontal_margin"

    android:paddingRight="@dimen/activity_horizontal_margin"

    android:paddingTop="@dimen/activity_vertical_margin"

    tools:context="com.kunai.switchtest.MainActivity">

    <TextView

        android:layout_width="wrap_content"

        android:layout_height="wrap_content"

        android:text="Themed Switch" />

    <Switch

        android:id="@+id/switch_item3"

        android:layout_width="wrap_content"

        android:layout_height="46dp"

        android:layout_alignParentEnd="true"

        android:layout_marginEnd="16dp"

        android:checked="true"

        android:longClickable="false"

        android:textOff="OFF"

        android:textOn="ON"/>

</RelativeLayout>

<RelativeLayout

    android:layout_width="match_parent"

    android:layout_height="wrap_content"

    android:paddingBottom="@dimen/activity_vertical_margin"

    android:paddingLeft="@dimen/activity_horizontal_margin"

    android:paddingRight="@dimen/activity_horizontal_margin"

    android:paddingTop="@dimen/activity_vertical_margin"

    tools:context="com.kunai.switchtest.MainActivity">

    <TextView

        android:layout_width="wrap_content"

        android:layout_height="wrap_content"

        android:text="'Styled' Switch" />

    <Switch

        android:id="@+id/switch_item4"

        android:layout_width="wrap_content"

        android:layout_height="46dp"

        android:layout_alignParentEnd="true"

        android:layout_marginEnd="16dp"

        android:checked="true"

        android:longClickable="false"

        android:textOff="OFF"

        android:textOn="ON"

        android:theme="@style/BrandedSwitch"/>

</RelativeLayout>

<RelativeLayout

    android:layout_width="match_parent"

    android:layout_height="wrap_content"

    android:paddingBottom="@dimen/activity_vertical_margin"

    android:paddingLeft="@dimen/activity_horizontal_margin"

    android:paddingRight="@dimen/activity_horizontal_margin"

    android:paddingTop="@dimen/activity_vertical_margin"

    tools:context="com.kunai.switchtest.MainActivity">

    <TextView

        android:layout_width="wrap_content"

        android:layout_height="wrap_content"

        android:text="'Styled' CheckBox" />

    <CheckBox

        android:id="@+id/checkbox"

        android:layout_width="wrap_content"

        android:layout_height="46dp"

        android:layout_alignParentEnd="true"

        android:layout_marginEnd="16dp"

        android:checked="true"

        android:longClickable="false"

        android:theme="@style/BrandedCheckBox"/>

</RelativeLayout>

<RelativeLayout

    android:layout_width="match_parent"

    android:layout_height="wrap_content"

    android:paddingBottom="@dimen/activity_vertical_margin"

    android:paddingLeft="@dimen/activity_horizontal_margin"

    android:paddingRight="@dimen/activity_horizontal_margin"

    android:paddingTop="@dimen/activity_vertical_margin"

    tools:context="com.kunai.switchtest.MainActivity">

    <TextView

        android:layout_width="wrap_content"

        android:layout_height="wrap_content"

        android:text="Themed CheckBox" />

    <CheckBox

        android:id="@+id/checkbox2"

        android:layout_width="wrap_content"

        android:layout_height="46dp"android:layout_alignParentEnd="true"android:layout_marginEnd="16dp"android:checked="true"android:longClickable="false"/></RelativeLayout>

styles.xml...

<resources>

<!-- Base application theme. -->

<style name="AppTheme" parent="Theme.AppCompat.Light.DarkActionBar">

    <!-- Customize your theme here. -->

    <item name="colorPrimary">#3F51B5</item>

    <item name="colorPrimaryDark">#303F9F</item>

    <item name="colorAccent">#FF4081</item>

</style>

<style name="BrandedSwitch.control" parent="Theme.AppCompat.Light">

    <!-- active thumb & track color (30% transparency) -->

    <item name="colorControlActivated">#e6e600</item>

    <item name="colorSwitchThumbNormal">#cc0000</item>

</style>

<style name="BrandedSwitch.text" parent="Theme.AppCompat.Light">

    <item name="android:textColor">#ffa000</item>

    <item name="android:textSize">9dp</item>

</style>

<style name="BrandedCheckBox" parent="AppTheme">

    <item name="colorAccent">#aaf000</item>

    <item name="colorControlNormal">#ff0000</item>

</style>

<style name="BrandedSwitch" parent="AppTheme">

    <item name="colorAccent">#39ac39</item>

</style>

I know, I know, you are too lazy to build this, you just want to get your code written and check it in so you can close this pain in the ass Android compatibility nightmare bug so that the designer on your team will finally be happy. I get it. Here's what it looks like when you run it...

API_21:

API_18: