The easiest way to add an artist to your watchlist is to click on the 'Add artist' link under the 'My Watchlist' menu. (Remember, you need to be logged in to view this menu!)  From here you will be presented with search form to find the artist.  When you have found the artist you want to add, click on the artist name which takes you to the 'Artist Details' page, then click on 'Add' next to 'Add to your watchlist'.

You can also get to the 'Artist Details' page (and therefore, the 'Add to your watchlist' link) by clicking on the artists name, wherever the artists name is listed on the site, eg. next to an artwork for that artist.  You can also get to this page by using the 'Artist Search' page - click on the 'Artists' link under the main menu.