It takes as long as it takes a moderator to approve it. We have 30-something moderators capable of approving posts, so generally it doesn't take all that long, but there are days when there are fewer of us.
Don't forget, we have to filter appropriate and inappropriate posts too. Members of GTP won't have seen any advertising, Cialis or pornography in something like 3 years - but we still have to dig through it.
This is also a period of interest in GT, so we have more new members every day now than 6 months since - our workload has increased. Ultimately, though, if your message is acceptable and we have no particular concerns over it (spammers have a certain MO which is tough to ascertain sometimes), it'll probably hit the site before a day has gone by.
We also currently have an automated system which may send messages even from approved users to the mod queue. The more we use the system, the more it learns what we allow and don't - so if you have subsequent message sent to the queue, you're helping the security of the site 👍