Please note that these examples do not use an electroscope as the object being charged. An electroscope also has light gold leaves at the bottom which will move apart to show the presence of charges. These are just spherical conductors; they become charged but do not show any outward changes.
Conduction is when a charged object touches a neutral one to share its charge. Unlike polarization, conduction is a permanent charging method; the charges will remain on the object they were placed even after the source is removed.
Note that if the source had been a positive one, electrons would have moved from the neutral object into the positive source, leaving behind abandoned protons and making the charge become positive; since protons are too big to move, this is the only way both objects could become charged.
Sometimes the charged object comes in contact with a neutral object so large (such as the earth) it basically neutralizes any loose or extra charges. This special type of conduction is called grounding. Grounding is done by either adding or removing electrons, as protons cannot move!
If two neutral materials rub against each other, one of them picks up electrons from the other and gains a negative charge. The other loses electrons and becomes positive. This is friction charging.
Induction is when no contact occurs between a neutral object and charged source, but grounding is used to charge the object. The neutral object is brought near a charged source to polarize its charges. The object is then grounded to neutralize charges that are not near the source. Since electrons are either added or removed from the object, when the source is removed, the object is charged opposite to the source.
These examples use an electroscope as the object which will become charged: