First off
I know I have had a few emails recently saying pop round but I feel so needed. Sorry I left, I feel awful.

First off, just NO, NO, NO, NO, NO!!!!!!!!
Do not say: we need X amount of words to rank, do not say it is not possible, do not listen to outdated advice that still talks about numbers of words, no body dare mention the word DENSITY, or KEYWORD TAG while we are at it!!!!!!!! This is not the 90's people, not the 90's!!!!!
Just like any vertical - video, local, news etc... - the image vertical, and on top of that image search, needs handling like you are on your first date. Go in too heavy with every tactic you know and it may work, you may just get lucky with one; but, if you have: a game plan, understand the lady before hand, understand her hobbies, understand her likes and dislikes and know her job then all you need is the right words (normally, "So what do you do?" knowing she is in admin with questions already primed for the answer: "I'm in administration"), right moves at the right time and the night's a good one.
So children, if we are sitting comfortably, be prepared to be taken down a journey of discovery. There will be some long words - I warn you now - there may also be bit of geek and a tiny bit of science; but, don't give up, pick your self up and carry on. Go make a hot coco - ideally with marshmellows - ready? Then I will begin.
Please note: There are some things I just wont go into on this journey. Just like if someone asks people who use crayons to make pictures (graphic designers in my office :lol

how do I edit a picture! That too would be like there is no hope in this answer.
First off what is the image vertical and image search?
The fact no one has even mentioned the word vertical yet - to this question - astounds me. The amount of awful advice still floating around is just the sad state of anonymous critque by so called "Guru's" on the web as a whole.
The Image vertical, is when images are shown in - and amoung - the organics (search results you don't pay for) and the Knowledge Graph (detailed section of hyper-relevent information to the right of the main results on certain SERPs). Image search - in this case - is when you use Google Image search to search for pretty - usually - pictures.
The start of the jounrey:
Right now to understand fully Image search; this relies on several different aspects. All of which you have good control over.
Basic level:
As Google says - include good alt text and name the images correctly. Well thats awfully good advice there.

So if you have a image of a cat and you are wanting to get to the top of image search for a cat try this:
[color=#800080;]<img src="images/cats/white-cat.jpg" alt="White cat with black spots on it, licking its paws" />[/color]
Moderate level:
Now if that's all you do be prepared to fail. Google is what? Anybody? Aww a sea of blank faces - no Levi not a giant corporation which is slowly monetising more and more of its services, well....; but, an automated text, document and file indexing algothrium attached to several thousand databases and servers which gives you context based results when you ask it certain questions....well that's the theory.
So to truely understand image search forget keyword fixation (the only thing that matters is this head tail keyphrase and nothing else - not the 90's!!!!!), create a story around the image, that's right put text around it. That text should talk about white cats, blacks cats, white four legged felines, link to other articles about cats (themantically linked content), surrounded with Hyponyms, Meronymys, Antonyms and Synonyms - yes these where the big words I warned you about, and no Tim I didn't just make these up they are real words with real meanings.
Please note: there is more to this even still. The correct words in the correct code segments, content above the fold and yet even more exciting topics.
Junior advanced level:
Now with that IMO, we have the utter basics and best practises, let us move over to the more advanced techy side.
- Firstly, make sure you are not blocking your image directory - or that it is granted access through a block - via the robots.txt file.
- Secondly, make sure the page can be indexed.
- Thirdly, make sure the page doesn't use the noimageindex meta.
- Fourtly, make sure the page can have its links followed.
Senior Advanced level:
Now comes the science. There are 2 hidden aspects that can come in to play those being PageRank and the far more important TrustRank. "Wait a minuite here", I hear Tim shout, this is not a link! No Tim you are right...it is an image. But turn the Image into a link that when clicked loads a new page containing a larger version of the image, (including a section of copy around the image and a link back to the page). This will help these key metrics flow to this dedicated page.
Now is this the most indepth post I could write about this subject? No! It's the basics at every level. But, this will at least help you down the journey of starting your images to rank well for searches you deserve them to. Hell it may even help towards making image search actually useful.

Hope it helps.
Jaz
Terminology:
SERPs - Search Engine Result Pages.
Head tail - Keyphrase that has high(ish) search volume per month.
Keyword fixation - Not understanding modern SEO theory and living in the 90'S!!!!!!!
Synonyms - Words that have similar meanings.
Antonyms - Words that are the complete opposite.
Hyponyms - Words that incorperate different sub categories.
Meronymys - Words that belong to other things.