Same-sex marriage approved in the UK

Thanks for the quick lesson! If the bill passes the House of Lords, does it then immediately become law, or does it need a final signature/approval?

It needs the Royal Assent, which the monarch is required to give. However, she can take her sweet time (or not) with it to send a message that she does not like it (or does like it).

Also, voting in the House of Lords is more symbolic than anything since all it really does is delay passage since the Commons can force bills through after two (or maybe it's one) rejections from the Lords.