This is good advice. If you're intaking too much salt your body retains water more easily. Just cutting down on salt intake will help you feel better and lose some quick weight. Plus it has other health benefits (lowered blood pressure, etc.). Watching the carb intake is important too. You don't need to cut them out completely, but cut back and make sure you're eating healthier carbs (i.e. whole grain stuff).
Eating more vegetables is key too. Filling up on vegetables is great because they have miniscule calories compared to starchy foods. So just for example, if you were going out to eat, get broccoli or a side salad with your sandwich instead of fries. Far fewer calories, far fewer bad carbs, and it will still fill you up. Drink a lot of water too - 8 glasses a day should be good.
One thing about the veggies though - this is mostly green vegetables I'm talking about. Stuff like potatoes, rice, etc. is technically vegetable, but it falls under the starchy/carbs category.
Getting some daily fruit in is good too, but keep in mind that most fruits do contain sugar, so I'd say it's better to eat those earlier in the day when your body is still metabolizing as opposed to later at night when things have slowed down.
And yes, cardio AND weight training are both important, so don't skimp out on them. I lost 55 lbs. last year with just a multivitamin and a high protein, low calorie diet (and exercise too), so it's definitely possible to see great results without really touching the supplements...