Well believe it or not directly before you give your evidence !
You will be called as a witness and asked to swear on the bible at which point you ask to affirm instead, on the reverse of the oath card is usually the affirmation. No-one will think any less of you for asking to do so.
So they have an affirmation ready on the reverse of the card, just in case?
Is this also read by those who subscribe to Islam, Judaism etc. or are there alternatives to the bible that can be offered for followers of religions other than Christianity?
Yes you would be surprised how many people affirm - I always used to affirm instead of swear on bible when swearing my Affidavits or giving evidence.
There is an alternate wording for followers of other religions - again usually kept in one place in the front of the bible - easily accessible so the clerk is not caught out - and yes other books of religion are also kept at the court too. I find it strange that you find it surprising that courts cater for all religions.