Here's how a lot of designers export their image assets from Photoshop.
- Turn off the layers you don't want.
- Make a marquee selection that's bigger than the element you want to save.
- Choose Edit → Copy Merged.
- Choose File → New and press return The new document will be the correct size to hold the clipboard.
- Choose Edit → Paste. It'll be in the perfect place, because the document was sized to the clipboard.
- Choose File → Save for Web.
Steps 3, 4 and 5 are easier than they sound, because you can just hit: Shift Command-C, Command-N, Return, Command-V to do the entire thing. Or even set up an action to do it for you (I have an action for this I can give you, if you'd like).
Repeat the steps for every element you need.
I'm assuming some elements may contain several layers? That's why I'd advise using this method over others. If each element is one layer only, then you could use Photoshop’s Export Layers to Files script.
By choosing File → Scripts → Export Layers to Files each layer of your document will be saved as a separate file with a filename that matches the layer name. This means you’ll probably have to prepare your document by flattening everything down to bitmap layers for the elements you’d like to export — a time consuming process, but often quicker than using Copy Merged. It can also optionally trim the resulting file, if you’d like completely transparent areas to be removed.