The first step is to prepare yourself mentally. Then peel away all the foil or plastic capsule covering the cork and wipe the top. Mold and other gunk hang out on cork tops and can give the wine an odd taste. Always insert the helix in the center of the cork and be certain it is going straight in. Keep your tip sharp.
Sharp tips prevent cork bits.
Make sure the tip is aligned with the rest of the helix so that it is not boring its way down while the rest of the helix is tearing a wider hole. If something goes wrong, stop. Do not force the issue. If only half the cork is coming out, screw the helix in deeper. If it is pulling out the center only, remove the corkscrew and drill another hole where you can start over again, or screw the helix down the side and try to pull it from there.