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I don't how to get started.
It should be a platform game for iPhone with some kind of elevator from one floor to another.

Like a hotel with many floors and the player must go from bottom floor to top floor in each level.

I guess it depends how complex the platforming is. For instance, can the platforms be aligned on a grid, are they square, or do you need to use physics objects?. Is it a puzzle platformer, do you need to move things around to advance, like pushable crates to climb up onto etc etc?

Is the elevator really like an exit to the next level?, if so, how would the screen be laid out?

Really there's no issue with the type of game, AppGameKit can handle it - it's more a case of how complex the game idea is will detrement how quickly you can get it made. A simple grid system, jumping up to the elevator to proceed to the next level, that's not a big deal at all. Maybe a bit like Rainbow Islands, probably the best vertical scrolling platformer ever made, that had this rising water level that you had to beat to the top of the level. If your going for more physics based puzzles, then you might have to put in some work on a level editor, so you can set the position and properties of your physics objects. I mean, a grid based map format, the editor can be written in an afternoon, but one with free moving physics objects, complex collision, joints and links... well that's really more like a weeks work.

If this is your first project, I strongly advise going for an array based map, square collision, and simple gameplay - a lot like Rainbow Islands.

have a look at my MrOttoBeat WIP, it is a physics platformer.
like Rainbow Islands, you have to make your way up.

An array based map makes art and editing easy. The built in collision and physics commands in AppGameKit makes it quite easy to code the game too. I am currently doing this myself. Check out the tutorials on the official website. No link, I'm on my phone.

I use to define each element separately (platform, ladders, enemies, ropes, etc), give it an ID, define a TYPE for it (containing the relevant information, e.g. x,y position, size, status, sprite id, associated id of related sprites, speed, etc), and I declare an array for this type.
Separately I define a CSV, JSON or XML format and create a file for each level, in which position, size and other characteristics of each element are specified.
A render function reads the file and draws all elements on the screen.
This way I have a complete freedom on where putting the objects, the size of the objects, bahaviour.
Alternatively, you can use array and/or tile maps, but you are more constrained. I used very much tile maps in DarkBasicPro to build side-scrolling games.