Submitting Form Data with Many-to-Many Relationship

I'm quite confused about how to implement a many-to-many relationship and my domain model. Let's say I'm creating a recipe box web application and I have three tables called Category (categoryID, categoryName), RecipeCategory (categoryID, recipeID), and Recipes (recipeID, recipeName, recipeDescription). If I were to present this information as an ASP.NET application and wanted to insert a new recipe and category, am I responsible for writing the logic to insert the information in the RecipeCategory table OR is it possible to set RecipeCategory.categoryID and RecipeCategory.recipeID automatically with default values based on newly inserted records in the related tables? If I'm responsible for writing the logic to insert values in RecipeCategory.categoryID and RecipeCategory.recipeID is that a trigger ...