Start by searching for a recipe. You can use the dropdown menus and text search bar at the top. Note that text searches are filtered by the selected skill, if any.
Recipe names (both the big ones and the "Used in" ones) are clickable. Click to go straight to the single recipe page for that recipe.
When you've narrowed your search down to a single skill, ingredients become clickable and take on check boxes next to them. Click an ingredient to expand it, or use the checkbox to exclude that ingredient from your Shopping List.
When an ingredient is expanded, it will be crossed off. That is because it is assumed you will be obtaining that item by crafting it rather than buying it. The item's required tools and ingredients will expand in a box beneath.
If you'd like to completely exclude an ingredient from your Shopping List, uncheck its checkbox. When an item is unchecked, it cannot be expanded until it is checked again, and all its nested recipes will be collapsed.
To expand all ingredients for a recipe, use the A button in top left. If you have any recipes already open, the button changes to a C button, which collapses all recipes. The P button opens your Shopping List, factoring in all checked items or, if the items are expanded, the ingredients to make them.
Remember, the advanced calculation options only appear when viewing a single recipe.