There are two main modes of enforcing this separation: a casual separation and a truly private separation. Both have their advantages and disadvantages.
People who enforce a casual separation still generally use their real name when interacting online personally and professionally. Sometimes they may differentiate this in some way – such as referring to themselves as Chuck in personal profiles and postings, and Charles in professional dealings – and other times they may just create separate accounts for the personal and professional sides of their life, but leave the name the same. Having a casual separation means you still have to be fairly careful about how you act, even in your casual mode, since professional contacts will likely still see that material – but by making it clear it is your personal life it will at least retain some distance. On a positive note, many prospective employers and clients do like to see a little bit of humanity in their business dealings – so long as you aren’t being offensive or too over the top.
Using a pseudonym or alternate identity is a more secure way of ensuring the distinction between professional and personal personas online. In this case you’ll create entirely new accounts, using a pseudonym or internet handle, generally made with a new email account so that even the operators of the social media sites don’t know who you are. Some care is taken to write posts with different grammar or style, so that even those who know you well won’t recognize you. And in the most extreme circumstances you may even want to use a proxy, so that nothing short of a court subpoena can unveil your true identity. This is a good solution for those who want to be able to be completely liberated online, without the danger of impacting their professional demeanor. On the other hand, some care should be taken to infuse your professional presence with at least a bit of humanity – some pictures of you in daily life, fun quotes, or lists of favorite bands or books – so that you don’t look like you’re simply using the internet as a business tool, with no deeper connection to the world of social media and interaction.