Wasn't sure what to name this tutorial, but this is what we are going to learn how to do:
Step 1
Create a new document of decent size. We will crop out the extra later. Go ahead and make it a white background, you can delete that later if you wish as well. Pick a shape you want to use from the custom shapes menu (right under the text tool). I am using a heart for this tutorial, but whatever you want to use that will work.
Step 2
Rasterize the shape layer. Use your selection tool (top left tool) to select the top half of your object. If you want to free hand it to make a jagged edge use the lasso tool (next tool down). We are just going to do a straight one for simplicity.
Step 3
Now, right click inside your selection and choose "layer via cut". This is going to remove that section from the current layer and place it in a new one.

Once you have done that, use your move tool in the new layer to move the top half back into place, so it appears to be a solid object again.
Step 4
You will probably want to rename your layers something, so that you can keep track of what is going on. I didn't, but should have. Now, duplicate the "top half" layer again. Make the original "top half" layer invisible, so you can see what you are doing. Now, go to EDIT > TRANSFORM > ROTATE. It will put a box around your object and if you move your mouse to one of the corners on the right side, you should have a little curvy arrow. Click and rotate it up slightly.

Now click your move tool and it will ask you if you are finished or something like that and say yes. Now, move your top half so the edges on the left side kinda match up like it is an opening box (like a hinge).
Step 5
Repeat step four, only rotate the top half just more than last time.
Step 6
Now, type your name in whatever font you wish, probably something not scripty, just block letters. Whatever size you want to use. Probably best if you type the text kinda at the top out of the way. Now, you want to make sure your letters are fairly far apart, so we can select them more easily. If you don't already know how to do this, go to WINDOW > CHARACTER. This will make your character box visible. Select your text and make the spacing 200.
Step 7
Rasterize your text. Now go to the selection tool again and make a box around the first letter, making sure it does not touch or include any of the other letters. Click on your move tool and then any of the arrow keys on your keyboard. This should highlight that letter only.
Step 8
You will want to go ahead and move all of your text layers underneath your object layers. That way the letter appears to be coming out of the object, instead of being in front of it. Move your first letter so it is halfway coming out of the object. Duplicate that layer and move it a little further on the path to where you want it. Duplicate once more and put it in the place you want it.
Step 9
Repeat steps 7 & 8 with each letter. You will want to hide all your previous letters, so you can see what you are doing, except each letters, final letter placement, as shown below.

Also, you may have to duplicate your letter one more time when you get further to the end of your word, so the animation runs smoother.
ON to ANIMATION
Get into image ready.
Step 10
First we need to open your object. Your first frame should be the "complete" or "whole" shape, the next frame slightly open and the third, all the way open. So that means you will need to have your bottom visible with each one of those tops in each frame.
Step 11
Duplicate your last frame with the "fully open" object and make your first letter visible that is coming out of it. The next frame should be that first letter in it's second position and so on, making sure to hide the previous position of the letter. Once you have your first letter in place, you will leave that visible, duplicate and move on to your next letter.
Step 12
Once you have all your word visible, we need to close your object. Duplicate your last frame and just start closing it, just like we did when we opened it, except we are leaving your word visible.
Step 13
Lastly, making the letters slowly disappear. When you have your object closed, duplicate and remove all your letters from visibility. Then hit the "tween" button, as circled below in your animation screen. The box shown will pop up, make sure all the settings are the same, except change the number of frames to duplicate to...ohhhh, 30. Okay, hit play!!!
Once you get this down, you can add different layer styles and such to dress it up.
Good luck and as always, ask questions!