How long does it generally take for a review to show up after it's been submitted?

Generally no more than 24 hours...

Sometimes they take a few hours. Sometimes a couple days.

Ah, okay. I'll stop refreshing the reviews page every 15 minutes then. I'm excited to have my review cherry popped!

Mmm, it's been about a day. So maybe it'll be up sooon?  

Yay. I'm excited for you!!! I was so thirsty to get my review cherry popped. Lol.  

good luck. You do need to be patient.

I have a few comments though, not to discourage you but just to prepare you just in case the review doesn't post.  
1) Some guys say they will review you, or say they did review you but they never do. I don't know why, but it happens. Maybe they got lazy, or busy, or maybe they just didn't want to write a review but it's easier for them to say they did write it and TER rejected it than to admit they never wrote it.
2) If the review was written and submitted, hopefully he followed all the rules. TER will reject rules that don't follow their guidelines. They are not terribly complicated guidelines but they are in place and must be followed. Many reviews get rejected for simple things that were outside of the guidelines. Many of these can be edited and resubmitted.
3) if you were this person's first review, it may get rejected because many times TER does not allow a first time reviewer to write a lady's first review. This is to help cut down on fakes and shills. Your first review should come from someone who already has submitted a few reviews. A reviewer's first review should be of a lady who already has some reviews.  

Re: good luck. You do need to be patient.

I've had reviews rejected.  One for not enough detail.  One because the provider didn't have a current web link.  I added detail on the one and informed to provider to get a link, which she did.  Both reviews were then accepted on resubmission.

Sorry, just caught this:
"TER will reject rules that don't follow their guidelines." This of course should say, "TER will reject REVIEWS that don't follow their guidelines." I assume everyone figured that out.
There is also an "of" that should be an "if" lower on the post.

He has many powers, but cannot moderate posters or remove posts at will.  If he did, Fancy would be toast.

If ANYBODY here was the NB mod, Fancy would be toast.

Just that ps wasn't.