simple: use the selection tool, draw a box or circle or freehand what you want to cut out, and then either go up to edit and then click cut, or type ctrl + c. There's a ****load of keyboard shortcuts for photoshop which make things go quicker if you know what youre doing. Remember, holding down on most of the tools in the toolbar will yield a subdirectory of other tools, and holding alt, shift, and control for most any tool will apply a certain property. For example if you have the square selection tool selected, and you hold shift and draw, it will constrain proportions to make a perfect square no matter what size it is.
I use photoshop a lot at work doing photo restorations... I find myself using the Clone tool more than anything. If you cut something out of a picture, white will replace it. If you want to cover up that white, you need the clone tool to copy little bits of the surrounding image into that area. it can get tricky.