These maneuvers are aerodynamically the same: opposite rudder to the current aileron. The named direction of the slip is based on the aileron, so right aileron and left rudder would be a right slip.

Forward slips are used to lose altitude without gaining airspeed while traveling across the ground in the desired direction. For example, I’m turning from left base to final to runway 25 (“two-five”) at Sewanee (KUOS). I’m high, so I’m going to do a left forward slip to lose altitude (left, since I was already in a left bank and that slight tailwind is from the left, slip into the wind). With the throttle at idle, I’ll hold left aileron and right rudder, balancing them to keep my ground track along the final course to the runway. More aileron requires more opposite rudder and gives a steeper descent angle and more of a “sideways” flight with the heading even farther off to the right. I’ll set the pitch attitude to keep from losing or gaining too much airspeed. The plane is traveling along the final course, but pointing off to the right. I’m watching my aim point on the runway to see how all of this is working out.

Static port location on the plane and having the pitot tube pointed off from the slipstream can affect indicated airspeed (IAS). My airplane has static ports on both sides of the nose, so the indicated airspeed in a strong slip doesn’t change too dramatically when I recover. An airplane with a static port on one side only (example, Cessna 152, left side) will tend to indicate a lower airspeed while in a left slip than in an identical right slip. When recovered from the left one, the indicated airspeed will move higher than what I had in the slip. Using the pitch sight picture, along with air noise, should help keep me out of trouble, anyway.

Side slips, on the other hand, are most commonly used close to the ground to offset a crosswind’s tendency to push the plane toward the downwind side of the runway. The goal in landing is to touch down with the airplane both aligned with the runway centerline and traveling down that line. Using a sideslip with the upwind wing down just enough to offset the crosswind component and with enough opposite rudder to keep the nose aligned with the runway will allow a touchdown with no side load on the landing gear. The upwind main gear touches, followed naturally by the downwind main, then the nose gear (tricycle gear). Of course, if the wind is constantly changing, this can be difficult to do just right (and I’ll be the last to claim that I get that many “just right”). The point is to do your best to take care of the airplane and its landing gear. You could do a side slip as soon as you turn final, but that’s a lot of time with everyone in the airplane leaning away from the slip. See the high quality illustration of side slipping on a 3-mile final. 

If you think of the side slip as off-setting wind and the forward slip as losing altitude, these two slips can be used together (left traffic, in this example): There’s a bit of tailwind on base. I’m a little high AND have let the wind blow me slightly downwind of the final course (if I’m a lot downwind of the final, I should go around, it’s the safe and smart thing to do). So, I lower the upwind (left) wing, put in opposite rudder and do a left forward/side slip combo, angling upwind to both get back on the proper final course and lose that extra altitude. I then have some choices after I’m back on course. If still high, I can continue forward slipping down the final course to lose altitude. If on a good glide path, and still well above flare height, I can go to coordinated flight and take up the proper crab to offset the crosswind, before assuming a sideslip as I get close to the ground. If it finally dawns on me that I’ve been doing a whole lot of maneuvering on this approach, I really should go around and do a better job next time earlier on in the pattern. Good landings are almost always preceded by stable approaches.

Some planes are prohibited (or recommended away) from slipping with flaps or full flaps. I suppose this refers to forward slips, not sideslips close to the ground to offset a crosswind. Check you POH or AFM for that info.

  Remember that when transitioning from coordinated flight to a sideslip to offset a crosswind, you can expect an increase in sink rate.