As it was already mentioned, that Layer Slider has many predefined skins, which you can select in the Slider Settings, under the Appearance tab. ALl of these skins have a CSS file, and these files can be modified with this tool. It has a very user-friendly interface:
In the top right corner you can see a selectbox. Here you need to find the skin, which you would like to edit. If you are not sure about that, you can check which skin has selected for your slider, by navigate back to the slider list, click on the slider to edit, and check the Skin parameter in Slider Settings Appearance tab.
Right under the selectbox, there is a full-width editor, where you can freely edit, modify or even add styles and definitions. After you finish with the modification, don't forget to click on the Save button.
Please note, that built-in skins will be overwritten by extension updates. Making changes should be done through the Custom Styles Editor.