I don't think this question has been asked before. However, the 'How do you deal with missing players' question is related.
My group just started a new campaign. A player we thought would no longer be able to play has had a change of circumstances and she is now able to continue with us which is excellent. We have had one session so far, which she did not attend.
At the beginning of the session the group will be underground on an isolated island, making finding another adventurer in the local tavern unlikely. I would like the player to be able to join in as soon as possible. The easiest but probably least satisfying option would be simply to say that the character had been there all along, and was with them for the duration of the first session. This would allow the player to join in immediately but, this would most likely reduce immersion and believability. At the other end of the spectrum the player could wait until the party reaches civilisation where they will join them which would be plausible but would mean the player waiting for the rest of the group.
How can I place this new character into the campaign in a realistic and quick way?