Firstly, the bell push wire will need to be removed from the screw connections on the bell push barrel.
This is will allow easier access to the lampholder.
Although illuminated pushes are available in all manner of designs, shapes and finishes, the lampholder will always be inside a white round 'barrel' as in the image shown below;
The white lampholder will now need to be separated from the front clear part. The two parts fit together with a 2 pin bayonet type arrangement and as such will need to be turned counter clockwise in order to separate.
.
TIP: It may help to relate this action to that of of removing a BC type light bulb from it's lamp holder!
Once separated, you can clearly see how the lamp sits within it's copper support contacts- Note how the bulb's 'legs' are bent back over and are each inline with a contact plate each side
The old bulb is now accessible and able to be removed. You may need tweezers to undertake this if it helps, the bulb simply lifts out vertically.
The replacement bulb's are available in a sealed twin blister pack. The Byron code for this is '4003'
Fitting the new bulb is a reversal of the process mentioned above.