What your instructor did was edit the part file he had saved in the assembly. The assembly file holds references to the parts that are in it. So when you change the part, it changes in your assembly. You could just create a part and then insert it into the assembly (the dialogue to insert should automatically open when you start an assembly).
Or, in your assembly press the "s" key, you should see this:
Pick the new part option.
Save your part to the desired location and build your part directly in the assembly. You can also right click the part in the assembly and edit it directly from there without having to open the part file. This is good for smaller assemblies, I work with very large ones and I tend not to try to create parts directly in assemblies or edit them through the assembly just because it makes the computer work hard.