Cutting out an image in Photoshop is a common thing to do, especially when working with photos. There are a few ways to cut out a photo but by far the best for precisely cutting out your image is the polygon lasso tool, check out the image below to see where you can find this tool:

Next we need to get our photo that needs cutting out, I just got a photo of a sign:

Now you just simply use the polygon lasso tool, by just clicking the next spot you want the selection to go around. In the image below, it shows how I started cutting out using the polygon lasso tool. The red circles show where I clicked:

If you need to zoom right in on your photo to do your cutting out, this next tip is something you will want to know. When you want to move across or down/up to continue your selection, you can temporarily use the hand tool to move around and then continue your selecting. To do this, all you have to do is hold down your SPACEBAR and after you have moved to the next part you want to select, let go of the SPACEBAR and continue your selection. See below:

After you have selected everything you will have a selection that looks something like this:

If you press delete now, you will delete the part you want, so you will need to inverse your selection, you can do this under the select menu(shown below) or you can use the keyboard shortcut, CTRL + SHIFT + I:

The selection should turn out like this (notice the selection around the outside):

Now press delete and you will have a cut out image that you can add a background to or what ever you like.