Upgrade SQLite database from one version to another?

I am getting an error from Logcat saying that a certain column (in my SQLiteOpenHelper subclass) does not exist. I thought I could upgrade the database by changing the DATABASE_CREATE string. But apparently not, so how can I (step-by-step) upgrade my SQLite Database from version 1 to version 2?

I apologize if the question seems "noobish", but I am still learning about Android.

@Pentium10 This is what I do in onUpgrade:

private static final int DATABASE_VERSION = 1;

....

switch (upgradeVersion) {
case 1:
    db.execSQL("ALTER TABLE task ADD body TEXT");
    upgradeVersion = 2;
    break;
}

...