Valid for Moodle 2.8. Updated on 5/26/2015.
Adding a syllabus is just like adding any other file. There are a couple of variations but the simplest approach is to turn on editing using the button, in the upper right or the link under Course Administration in the Administration block and then dragging the syllabus file from your computer to the Moodle window in your browser. You can only add files near the bottom of a section in your course. You'll know you've dragged to the correct place when a Add file(s) here message appears.
Once you've added your file you can move it to another location in your course using either the or icon depending on which appears to the left of the file name. You can drag and drop the first icon to move your syllabus. With the second style of icon you'll get a set of empty boxes and you click on the one in the location you want put the syllabus.
Initially the file name of your syllabus will be displayed. You can change this by using the icon that follows your syllabus.