Since you are already living in your condo, your options are not as wide open as they would be in new construction. Typically, there will be two walls between you and your neighbor. You will have your wall (drywall then framing - probably 2x4) then their wall. You can have an insulation contractor come in and do a "drill and blow", where they would actually drill a hole in the wall and blow fiberglass insulation to fill in the wall cavity. The other 'less atractive' option would be to take down your drywall and install regular fiberglass insulation batts. Good Luck.