There isn't really any "one click" solution and there are very many techniques for removing backgrounds, depending on your image. Here are a few solutions listed by difficulty + results from easiest/worst to hardest/best
Magic Wand Tool
The magic wand tool can be used to select chunks of color in an image. This is probably the closest you will get to a one click solution. Just select the color or multiple colors by using shift+click then mask or delete the unwanted pixels
The lasso tool
The lasso and polygonal lasso tools can be used to select a particular section of an image. This produces rough selections and is difficult to get very detailed with your selections. For the lasso tool just click and then draw around the areas you want to remove/mask. For the polygonal lasso tool click and move your mouse to create a line segment click again for another line segment, repeat this until you have outlined the entire section you want to remove then mask/delete.
The pen tool
This is my go to when I need to mask out an image. The pen tool has quite a high learning curve by produces the most accurate selections. It is a vector based tool so it can be used for vector masks, which are nice because you can go back and edit the mask as needed. Use the pen tool to draw a vector around your selection, right click and "make selection" or "Create vector Mask"
Levels, Curves and Channels
For masking finer pixel data such as hair and shadows there is another technique that involves using channels and levels to darken a part of an image in order to remove that darker area. A full write up is too long for this answer but you can read more about it in this detailed article
There are many different ways to mask an image in photoshop none are inherently better than another it just depends on how complex your background and foreground are and the result you are trying to achieve. If you just google "masking in photoshop" there are hundreds of thousands of good resources to get you started. Best of Luck
You can combine one of the techniques above with the refine mask tool in PS to get better results for things like masking hair. See the write up here
I tried to post some links for resources but stackexchange wouldn't let me. I'll post 2 here (the max) and the rest in the comments.