Generally, rinsing the electrode with distilled water after using should suffice. If the glass bulb looks dirty, you can rinse the electrode with warm water and a mild household dish washing detergent (not Alconox detergent).

If the electrode and bottle appear to have mold growing in or on them, you can clean with bleach to remove the mold.

1) Fill the storage bottle with a mixture of 1 part chlorine bleach to 3 or 4 parts water (careful! such a mixture is hazardous to your skin and eyes!) and soak the electrode for 8 minutes.
2) Thoroughly rinse both in cold or lukewarm water.
3) Refill the bottle with pH Storage Solution and return the sensor to the bottle.

In biological labs where proteins are used, the glass bulb can get fairly dirty. In this case, do the following:

1) Soak the electrode for 10-15 minutes in an acidic pepsin mixture. Approximately 5% pepsin in a 0.001 M HCl solution should work (pepsin can be purchased through Flinn Scientific, order code P0006).
2) Thoroughly rinse the both in warm tap water.
3) Refill the bottle with pH Storage Solution and return the sensor to the bottle.

Related:
Where do I get pH or ORP Storage Solution? (Buffer Storage Solution)
What do I do about mold growth in my bottle of pH electrode storage solution?
My pH Sensor has mold inside the shaft. How do I remove it?