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It sounds like you turned on the Talk Back mode. You can turn it off from Settings > Accessibility > Talk Back and turn it off.
When talk back is enabled, you will have to tap and double tap on the item to open or select them. For eg: If you want to unlock the screen, then you have to tap on the lock and then double tap on it to unlock. Or double tap on it and slide with two fingers to unlock. To open Settings app, tap on Settings and then double tap to open it.
You will also have trouble navigating through the screen. When Talk Back is enabled, use two fingers to scroll or swipe across the screen. Remember, it would take a little time to get to settings. So keep trying.
Please let me know if that didn't work, so we can continue troubleshooting.