The Library of Virginia (LVA) is the official library for the state and is a major repository of historical records for all of Virginia. If you hit a roadblock in your genealogical research locally, there is a chance that the LVA has records that can help you! Luckily, many of their historical records have been digitized and are available via their website, and many of their books are also available via your local library's Interlibrary Loan Service.
Additionally, if you are near Richmond or able to make the trip, they hold periodic workshops for beginning genealogists. You can learn more about these at this site.
To find information on a particular family in their online catalog it is recommended to search for "[last name] family."
If you visit them in Richmond, it is recommended to register for an account before you visit and then obtain a library card in person. You will need a card to page books from their closed stacks, and you will also need a Photo ID regardless to gain access to their materials. An on-site visit is also recommended as they have a large selection of print records, published genealogical histories, and other materials, organized in an easy to browse manner that is grouped by county. They also have materials from states surrounding Virginia.
If you need help, most of their staff has experience assisting genealogists and can point you towards the proper resources, but as with all of your research, you should gather as much information as you can beforehand using your own resources. This PDF is a great resource for how to get started and the numerous other guides listed under "Biographical and Genealogical" on their site are also a good way to help you get started.
Bottom line, if you are doing genealogical research in Virginia, the Library of Virginia is a one-stop shop and should be on your list of places to visit. They even have free garage parking directly under the library.