Cell lysis protocols are not the same but if you are interested in just western blotting, total protein lysate is adequate. You can obtain this by boiling your cells in lammeli buffer (protein sample buffer).
Other applications will require different buffers. For example, co-immuneprecipitation will require a more gentle non-denaturing (native) cell lysis buffer. Also, if you are interested in nuclear extract only you might want to use different lysis buffers to separate the cytoplasmic lystate from the nuclear extract. Hope this is helpful
As mentioned above, there will be some experiments where you may want to use different buffers to extract proteins only from certain organelles, i.e. mitochondria for mitochondrial proteins and plasma membrane fractions for plasma membrane proteins. However, depending on the question being asked, it may also be permissible to just do a simple whole-cell extraction i.e. using RIPA extraction. Abcam has a great guide to familiarize beginners with the nuances of Westerns;
The general rule during the whole cell protein extraction is to make the extraction buffer as close as possible to the maximum of the physiological activity of this protein (pH, salt concentration, the presence of possible inhibiting substances, and so on). Another factor you might want to consider is the presence of all necessary protease inhibitors to make sure that they can't destroy your protein after the cell lysis. That's why the use of the protease inhibitors cocktail containing the inhibitors to all natural proteases is highly recommended. And, of course, it would be nice if you had the info about the possible MW of your protein to make the right choice of the acrylamide concentration of your gel for western blotting.