I use the newest version of Photoshop, so it might look a tad different then the version you are using. If that's the case, no worries. The way to achieve your goal is still the same, and most everything looks the same as the older versions of Photoshop.
I'm not sure the subject matter you're working with, but I'm going to use my desktop background as reference for this. I've created an image with each of my icons on the desktop numbered, 1-9. Let's say your goal is to put icon 1, 3, 7, and 9 on an image together, without having all the other stuff there. Certainly this is not what you're doing, but it'll work as an example. Here's the original image;
Link: Image 1
So let's say you don't even know where the crop tool is, here's where;
Link: Crop Tool
The next step would be to draw a square around the first icon that you are wanting to use in your new piece, so you'd draw a square around icon 1. As seen below.
Link: Crop Selection
The problem you're going to face when using the crop tool to achieve the goal you're trying to achive, is that once you've completed selecting the cropped selection and you've either clicked the check-mark up near the top of the Photoshop screen, or pressed enter, it then discards the entire part of the remaining image that was not selected and leaves you with the following, as a new image, replacing the entire desktop containing the other icons you want to use.
Link: Cropped Image
Photoshop actually discards the rest of the image, so getting icon 3, 7, and 9 would require you to actually use the edit and undo function to get back to your original image. Then doing this, discards the section you cropped so you're right back at square one. To get all four icons on a new image, using the crop tool is actually the wrong way to go.
The way that you could get 1, 3, 7, and 9 on an image together, without having the rest of the icons or the entire unused section of the desktop, would be to use the selection tool and to copy and paste each thing you've selected, onto a new document that's set big enough to fit all four icons. So you'd want to have your original document you want to take images from, and also a new document that's blank, both open.
You'd want to use the selection tool and select the first icon, copy it, go to your blank document and paste it on there using either ctrl+v or the Edit --> Paste function on the Photoshop toolbar as seen below.
Link: Using Selection Tool
As you can see from that example, the selection tool was used to draw a selection area around the first icon. The icon was the copied and pasted onto the new document. You'd then need to select each separate icon you wanted to use and paste each one onto the new document until you had your finished product which would look like this;
Link: Finished Document
As you can see, all four icons you needed are now pasted onto one document together, without the rest of the original document included. Something not accomplishable with the crop tool.
Hope that helps.