The first step is to make sure the bolt which forms the pivot for the blade is tightened so there is no play between the blades. Of course, the blades must still move easily and the pivot should be kept oiled to prevent rust.
If the bolt or blades have worn, it may be necessary to replace the bolt possibly using one which is slightly larger in diameter. You can often do this by changing from an imperial bolt to a metric bolt or vice versa. Use a locking nut if possible so that the bolt doesn't loosen in use.
Then look at the way the blades have worn. Often the edges at the tips don't meet. The rub a few millimetres behind the edge so very little cutting takes place and grass trapped between the blade tips then separates the blade further reducing the cutting action.
If this is the case, grip the end of each blade in a vice and twist the blade a little until the edges of the tips meet rather than the faces. Use a mole wrench or similar (stillson wrench, large adjustable wrench) to apply the twisting action at the pivot end of each blade. I usually need several attempts to get the necessary twist in the blades but this is better than over twist them. Try to twist each blade the same amount.
It may be necessary to bend the blades very slightly towards each other but don't overdo this as it will greatly increase the rate at which they wear. do this by opening the jaws of the vice so that the are 1-2 inches apart and lever the blade about half way along as if to force the vice jaws apart. This creates a gradual bend in the blade rather than a sharp bend at one point. This is less likely to break the blade. The bend should be almost imperceptible being just visible if you sight along the edge from the pointed end (be careful doing this!).
Then grip the back (non-cutting) edge of each blade in a vice so that the cutting edge is clear of the vice jaws and horizontal with the cutting edge away from you. Use a fine file set so that it slopes upwards at between 10 and 15 degrees and gently file along the edge to create a good cutting edge. 2-3 strokes are usually enough as the blades are thin. Try to keep the angle of the file constant while doing this so the the angled face of the blade is flat and not curved.
Filing the edge creates a burr on the face side of the edge so use an oilstone to rub flat against the blade face to remove this burr. Don't rub the oilstone at an angle to the face as this will destroy the cutting edge but it is OK to rub it flat on the face of the blade.
The shears should now be as good as new and will cut easily and cleanly.
I hope my description of the process is clear enough to understand. If you don't have a file, an oilstone could be used but it is difficult to hold steadily and your hands are at a greater risk of being cut by the blades. If you don't have an engineers vice, you might be able to clamp the blade to the edge of a table but sharpening will be more difficult. I wouldn't try bending or twisting the blades without using a vice as the forces required are quite large and it would be easy to injure yourself if the shears slip.