The "slingshot effect" or gravity assist involves a vessel robbing angular momentum from a large body.
If you launch a vessel towards a planet (so that you come near but don't collide with it), then in the reference frame of the planet your vessel will leave with the same velocity going away from the planet as the velocity of your approach. However, since the planet was moving with respect to the Sun, you will have gained or lost velocity with respect to the Sun, depending on whether your space craft approached from behind or in front of the moving planet. Typically in these assist maneuvers, you wait for a large planet to be a bit ahead of the Earth's orbit. You launch towards that planet, and the gravity assist accelerates the space probe. Some of that acceleration will be tangential (mostly useless to you) but some will be radial, increasing your velocity from the Sun.
The Voyager probes took advantage of a once-in-every 180 year planetary alignment, with all of the outer planets mostly aligned. See http://en.wikipedia.org/wiki/File:Voyager_2_path.png for a good illustration. All the outer planets are traveling in a counter clockwise direction, and you can clearly see the outer planets accelerating Voyager 2 tangentially. It should be clear that there will be a radial component to that acceleration as well.
I don't think you can use the Sun in these circumstances; it doesn't have any angular momentum for you to steal.
Incidentally, the discovery of this method is sheer brilliance; without using gravity assists it would have taken prohibitively long and required a prohibitive amount of propellant to reach the outer planets.
A theoretical and probably ridiculous question here, but... does not the probe thus reduce the planetary orbital speed by the same amount (relative to mass, I guess), that it gains?
Momentum is conserved in the system (total momentum of probe and planet is always the same). Momentum = mass x velocity, so yes, the planet will slow down, but it's a ridiculously small amount. Think of shooting airgun pellets at a tank barelling down on you to slow it down, but even less effective.
If you launch a vessel towards a planet (so that you come near but don't collide with it), then in the reference frame of the planet your vessel will leave with the same velocity going away from the planet as the velocity of your approach. However, since the planet was moving with respect to the Sun, you will have gained or lost velocity with respect to the Sun, depending on whether your space craft approached from behind or in front of the moving planet. Typically in these assist maneuvers, you wait for a large planet to be a bit ahead of the Earth's orbit. You launch towards that planet, and the gravity assist accelerates the space probe. Some of that acceleration will be tangential (mostly useless to you) but some will be radial, increasing your velocity from the Sun.
The Voyager probes took advantage of a once-in-every 180 year planetary alignment, with all of the outer planets mostly aligned. See http://en.wikipedia.org/wiki/File:Voyager_2_path.png for a good illustration. All the outer planets are traveling in a counter clockwise direction, and you can clearly see the outer planets accelerating Voyager 2 tangentially. It should be clear that there will be a radial component to that acceleration as well.
I don't think you can use the Sun in these circumstances; it doesn't have any angular momentum for you to steal.
Incidentally, the discovery of this method is sheer brilliance; without using gravity assists it would have taken prohibitively long and required a prohibitive amount of propellant to reach the outer planets.