You need to add your layout inside a Scrollview, thus:
<ScrollView xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    >
    <LinearLayout
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        android:orientation="vertical"
        >
        <!-- Todo o restante do seu conteúdo -->
    </LinearLayout>
</ScrollView>
That way, in case the contents of your LinearLayout does not fit on the screen, Android itself will try to make the screen slidable.
Addendum:
Note that Scrollview accepts ONLY ONE direct child, that is, only one layout can have Scrollview as direct parent. In the example I posted, this Layout is the Linearlayout.
For example, you can’t do something like this in Scrollview:
<ScrollView xmlns:android="http://schemas.android.com/apk/res/android"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        >
        <LinearLayout
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            android:orientation="vertical"
            >
            <!-- Todo o restante do seu conteúdo -->
        </LinearLayout>
        <LinearLayout
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            android:orientation="vertical"
            >
        </LinearLayout>
    </ScrollView>