Marquee
This is most straightforward selection tool, the Marquee allows you to draw a box as well as a circle, column, or row around a section of your image, and select everything in that section. By default, the Rectangular Marquee is the primary tool that is visible in your toolkit, but if you click and hold on the icon, a submenu will appear with the other Marquee tools. To quickly access the Marquee, just press the M key, and to switch to the other Marquee tools, you can press Shift+M.
Quick Selection
The Quick Selection tool is one of the new addition to the Photoshop toolkit, and it allows you to paint a selection just like a brush, with options for brush hardness, size, and more. Just paint around the target area, and Photoshop will identify the edges of your selection. For even more finesse and accuracy, you can enable the "Refine Edge" and "Auto-Enhance" settings on the top options bar.
Magic Wand
Normally, the Magic Wand isn't the right tool for the job, because it measures color and contrast when making your selection. It's good when selecting objects that have an extreme color contrast with the background, but for a more complex selection, you may want to use one of the other tools. Fortunately, Photoshop's developers have included a "Refine Edge" setting on the Magic Wand options bar as well, and this does an excellent job of cleaning up a proper selection.
Color Range
Like the Magic Wand, the Color Range tool lets you target specific colors in an image, and then select them all. To access this tool, go to Select > Color Range and a new dialog box will appear. Then, select the eyedropper icon and click on a color in your image to target it. It shows a preview in the dialog box, and all of the selected areas will be white.
Lasso
This is Similar to the Marquee, the Lasso tool offers a freeform approach to drawing your selection. Once you have completed a lasso shape, Photoshop will analyze the image and adjust your lasso selection so that it matches more cleanly. This is the second fastest way to select, but it often leads to sloppy results. Depending on the situation, you may want to use these other Lasso tools like Polygon Lasso or Magnetic Lasso.
Pen Tool
The Pen tool allows you to create paths, which can then be converted to selections by pressing Command + Click. This is probably the most accurate selection tool since it can draw smooth curves and shapes. With this pen tool, you'll need to get comfortable creating entirely manual paths. Instead of freehand drawing, the main Pen tool uses anchor points and direction lines to determine the selection. At the same, there's also a Freeform Pen tool, which automatically creates anchor points as you draw a path.