Mainly through article content, but also some maintenance work, such as tagging article talk pages with the project banner, and answering queries on the talk page. Most of this is carried out by DBD (talk·contribs) (project founder I believe), but most members chip in wherever work is necessary.
Which do you consider your best contributions to the Project?
Personally my best contributions are three featured articles for the project, here, here, and here. Another should be finished shortly, but I've been waiting on a necessary source for quite some time. Otherwise there have been some more minor articles, a DYK, and many article fixes. The principle article writer for the project is probably DrKiernan (talk·contribs), who has given the projects many featured articles.
Which areas of the topic are best covered by the WikiProject?
British Royalty, which is quite a wide scope (1714 to the present day). This includes all members of the royal family who at one stage bore the style Highness, Royal Highness, or Majesty. At present there are 219 articles under this project, which is a sister project of Wikipedia:WikiProject Royalty.
What are the achievements of the WikiProject so far, and which goals has it set itself?
The achievements of the project is seen in the assessed article count primarily. Out of 219 articles, 19 are featured, four are good, and 49 are "B"-class. A number of the project's articles have appeared on the main page as the today's featured article or as DYKs. As far as I know the project has set itself four goals at Wikipedia:WikiProject British Royalty/To do, which are: "attract more members!; discuss what should be included, what not, or how to organise the information; discuss how to section large articles; establish guidelines". Other goals include assessing unassessed articles, keep categories and templates up to date, and, of course, developing content.
How could one get involved in the WikiProject?
There are a number of ways you could help out. Take a look at the home page at Wikipedia:WikiProject British Royalty for the basics, which includes the current scope and guidelines. Building content is always the most valuable involvement, and we have some top and high importance articles that need improvement here. Otherwise, being available to answer queries on the talk pages, or checking article assessments and categories, would be a great help. Remember to sign up here if you're interested!