If your plane isn't working as smoothly as it should, it may be that sticky wood resin has collected on the sole. Remove it with paint thinner. To keep the resin from collecting in the first place, apply paste wax regularly to the sole.
To prevent the edge of your work from splintering, clamp a section of scrap board to it and plane the two pieces at the same time.
Always plane with the grain, not against it. To determine which way that is, look at the edge of the wood; the grain's pattern will be angled, not straight. 'With the grain' means in the direction of this pattern.
To make a perfect square edge, attach a guide to the sole of the plane. Choose a piece of wood at least as long as the plane and position it flush with the edge of the plane iron so that it forms a square that can ride along the face of the work. Clamp it in place or drill two holes through the sole and screw it on.