The Adafruit GFX library is used for LCD handling:

To initialize the UI_Lib:

Create an Adafruit display object depending on the used display (e.g. ILI9341, ST7735, ...).
Init the display object accordingly.
Call the UI_Manager::Init function of the UI_Manager (use the UiManager instance delivered with the library) with the created Adafruit_GFX object.
Optional: Configure the colors you want to use with the UI_Manager::SetColors method. It is also possible to set the colors individually with the UI_Manager::ColorBackground, UI_Manager::ColorForeground, UI_Manager::ColorForegroundEditMode and UI_Manager::ColorFocusFrame properties.
Optional: Configure the font you want to use with the UI_Manager::SetFont method.

At this point, nothing is displayed yet. There is no visual tree assigned (and created) that can be shown, so create one:

Create objects of all UI elements that you want to use to build the user interface (CAUTION: some UIElement objects use dynamic memory allocation using the new keyword. More details can be found in the core implementation page).
Link all objects to their parent objects (e.g. add a NumericControl to the item collection of a ContainerPage, add the ContainerPage to a ContainerTabs, ...) by using the appropriate functions of the parent controls.
Connect the root of the visual tree to the UI_Manager by using the UI_Manager::ChangeVisualTreeRoot method.
Call the UI_Manager::Draw method whenever you want to update the screen. The library decides if something changed and if the screen needs to be redrawn (to reduce flickering).

Now the user interface is shown but no user inputs are processed.

You have to feed the UI_Manager::KeyInput function whenever a key was pressed. Rotary encoder inputs should also be encoded as key presses (KEYUP, KEYDOWN, KEYOK). This library is not responsible for detecting key presses.
You have to feed the UI_Manager::TouchInput function whenever a touch on the display was made. This library is not responsible for detecting touches.