Cleaning and oiling a Singer 3002
Most of the time you don't need a cleaning manual dedicated to the specific machine. What you need is a basic understanding what cleaning and oiling is intended to achieve and what the mechanical parts of the machine have to do with it.
Sewing machines, especially the older models without electronics, are masterpieces of mechanics. The rotation of one single motor is transferred to the base of the machine and the needle, and additionally translated into different needle positions that create sewing patterns. The top thread is transported into the bobbin case by the needle and must slide smoothly around the bobbin. All these movements should me as smooth and unimpeded as possible for the machine to work well.
What could impede these delicate movements is: lint, dust and old oil.
To clean the machine you gradually remove all removable covers and parts to access the mechanical innards. How to do this depends on your individual machine. Keep screws and small parts in a saucer or small bowl so you won't lose any. Open and clean one section after another, then put all removable parts back in and close the cover before opening the next part to not confuse any parts. The main sections to open and clean are:

The base, including the bobbin case, feed dog and needle plate itself (most often opened from the side you sit in front of)
The sewing arm (most often opened from the top)
The needle holder and mechanics just above it, including the lamp (sometimes opened from the side, sometimes from the top)

Hopefully the instruction manual contains instructions on how to open the machine. I was unable to find any material explaining how to open and maintain a Singer 3002.
The cleaning itself is simple: Carefully remove all dust and lint using either a soft cloth, dry brush or a gentle vacuum. The cloth can be dry or slightly dampened with clean water. Detergents or other cleaning products are not required.
Usually it's sufficient to wipe oiled parts off to remove the outer layer of oil that caught dust and lint particles. Use the hand wheel to slowly move the parts and wipe any old oil away that you couldn't access before. Then add a drop of fresh oil and you're basically done. You should only use special machine oil or mineral oil for sewing machines, because it stays liquid for a very long time. Organic oils become rancid and viscous over time and are not suited for sewing machines.