How to split the screen with two equal LinearLayouts?

Use the layout_weight attribute. The layout will roughly look like this:

<LinearLayout android:orientation="horizontal"
    android:layout_height="fill_parent" 
    android:layout_width="fill_parent">

    <LinearLayout 
        android:layout_weight="1" 
        android:layout_height="fill_parent" 
        android:layout_width="0dp"/>

    <LinearLayout 
        android:layout_weight="1" 
        android:layout_height="fill_parent" 
        android:layout_width="0dp"/>

</LinearLayout>