Every few weeks you should put a drop of oil in the opening of the bobbin case (visible when the bobbin is out) after cleaning that area. (This is to the center front of the bobbin case.)
Every few months, you need to put oil (just a drop) on several points inside the face plate. One spot is high (near the thread take up lever when in its highest position). Then oil the upper shaft of the needle and presser foot mechanism and at the top of the section with the screw midway down the shaft (the farther back). Add a drop of oil at the bottom of the shafts (two spots), Additionally put a drop of oil farther right near the thread path.
Once a year, remove the top cover and place a drop of oil at both holes on the top. (One is near but to the right of the main spool pin; the other is near the thread guide at the take up lever.) Put a drop of oil at the hole at the center right of the deck of the sewing machine (right next to the motor and below the stitch width selector). With the top cover off, there are a number of spots that need oil. One is near the center of the machine at the take up lever (top of shaft). The next is at the center of the stitch width cam. Place another drop of oil at the top of the lever that rests against this cam. Place a drop of oil at the bottom of the lower gear (the one that turns in the horizontal plane). Also oil three points to the right of the vertical gear. (These are the two sections on the shaft to the right of the gear and the point in that same line just to the right of the screw to the back of the area.) Remove the bottom of the sewing machine and oil seven points (three to the left and 4 on the right). Do this carefully - you do not want to get oil on the motor or the belt. These points are on the left: on the shafts near screws at the top and bottom and one spot near the center just in front of the belt. For the points near the screws, the one further up is closer to the left edge of the nachine. On the right side: two points above the belt. One is right next to the belt and one is on the shaft below a screw (this shaft continues to the lowest oiling point on the left side).
The manual for the Singer 457 is available from Singer as a PDF: http://www.singerco.com/uploads/download/5d6ce627c00cb91c477d4703f1b704aab08a72c8.pdf
. See the diagrams starting on page 53 (page 55 of the pdf) for the exact oiling points. I tried to explain these spots but I usually grab the manual for the pictures for my machine for the yearly oiling. You can buy a copy of the manual from Singer for $15 here: http://www.singerco.com/accessories/instruction-manuals/
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I hope this helps.