Jupiter and Saturn are opposite sides of the same coin: Jupiter expands, is joyful, optimistic; Saturn contracts, is cautious, realistic. In the natal chart, Jupiter can show areas where we experience greater ease or "luck" in our lives, where things come more easily to us. Saturn shows the areas where we experience the greatest difficulties, the most challenges, and have the most to learn. Saturn is often a misunderstood planet, seen as highly negative, but really, he just wants us to learn life's lessons. In the natal chart, Saturn often shows the areas where we'll face challenges until "adulthood," or after we experience our first Saturn return in our late 20's/early 30's (it's when transit - moving - Saturn returns to the exact position it was at when you were born; it's seen as one of the aspects that signals the start of adulthood).
In prediction, wherever Jupiter is, we tend to have things fall into place with greater ease. Sometimes this will occur without you doing anything, but usually you have to put in even just a little effort. If you don't, then it'll usually manifest as laziness and missing opportunities. Jupiter going through the 1st house or in the sign of your Sun or Moon can also be good for losing weight (if you put in the effort) or gaining weight (if you don't). Saturn in prediction is tricky. Usually at first, he'll bring difficulty with the areas of life the house he's going through rules. This is because, again, he wants you to learn life's lessons, so if you haven't been behaving properly, making good decisions and being responsible, he'll force to. Any problems he brings tend to come in the first half of the transit. As he nears the end of a house, things tend to improve, especially if you've been working better, and if you're doing everything right, then you'll usually be rewarded. Saturn's hardest during his first tour through your houses; after your Saturn return, you enter the second tour, and it tends to get easier with each tour afterwards (because, obviously, you keep learning lessons and need him less).
Jupiter rules Sagittarius and the 9th house; Saturn rules Capricorn and the 10th house.
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