I have to place an Illustrator file into another one and then resize it (way smaller). How do I do that and keep a clear image?
If the file you're placing isn't too complex, you could just copy the paths in that file and paste them into the other.
You can also do File->Place and place the illustrator file. It should retain quality as Illustrator is a vector program, and you're placing one vector file into another. This will link the file, so if you go to Window->Links, it should give you a window that shows all linked files (similar to InDesign) and you can "Update Links" when you update the placed file. This is convenient if you're doing print layouts and need to have the logo saved elsewhere.
Hope that helps!