The traditional way for professional artists to gain a public profile and sell their art has generally centered around working with bricks-and-mortar galleries and perhaps with dealers, moving through set channels to establish a reputation and build up popularity.
Applying to galleries is a well-known process, and generally involves the submission of a portfolio of recent artwork, which is then reviewed by the gallery director and either accepted or rejected. Artist statements, biographies, and so on all play a role here.
This method is still important today, and gallery representation can be hugely beneficial to artists in their careers. It contributes to developing professional presence and is a valuable asset on a C.V. Yet it is no longer the only way of selling work, and many artists would do well to look into the relatively new process of advertising one's work through social media.
Word of mouth has always been an essential element of building up a successful artistic career, though it may have been less discussed in the past. There is nothing better than someone who has seen your work going away from it excited and telling all their friends about it. Similarly, a buyer who is thrilled with their purchase and puts it up on their wall for visitors to admire is unwittingly doing you a service as well as adding to their home dcor.
The increasing influence of social media allows you to encourage this process, and increase it, reaching people you might never have been able to contact otherwise. Participating on social media sites means that you can advertise your work in an informal, relaxed setting, and keep people up to date with where you are and what you are doing - the hunt you had to go on to find just the right materials, the trials of getting that difficult painting just right.
Moreover, when they do, those friends no longer have to rely on the enthusiasm of someone they know. Instead, they can have instant access to see what is being talked about, and if they are likewise impressed, can pass that on, and so on.
Online galleries such as Art-Mine feed into this trend, and are an excellent way for people to see what all the fuss is about. The images are generally far higher quality than on an ordinary site, and it is valuable for potential buyers to see your work in the context of a gallery setting. It is therefore worthwhile and important for you to make the link to your page on the gallery you belong to well-known, associated with your presence on social sites, so that your work, properly displayed, is only one click away.
Don't be scared of the newer ways of advertising yourself and your works. Selling through social means is just the same as it used to be, but with even greater possibilities - and with even greater potential for you to display yourself and your art at your best. Go for it!