When someone tries to send you a file, the file is displayed in your conversation window, as shown below.
If the file is a picture, you can choose to save it to your computer by right-clicking it and choosing Save as.
If the file is another type (a document, a spreadsheet, etc.), Skype will automatically download the file for you. You can double-click the file to open it, or you can choose to see where it's downloaded by right-clicking the file and choosing Show in folder.