Alston graduated from Averett University in 1979 and obtained his law degree from the North Carolina Central University School of Law in 1982. He began his career as a staff attorney for the National Labor Relations Board, a post he held for two years before going into private practice. In 1998, he was elected by the Virginia General Assembly to be a judge of the Juvenile and Domestic Relations District Court for the 31st Judicial District, encompassing Prince William County. He was elected to the Prince William County Circuit Court in 2001. While on the circuit court, he presided over the case of John Allen Muhammad, the mastermind of the D.C. sniper attacks, which brought him national attention. He was selected by his colleagues to be Chief Judge of the circuit court in 2007, when that position became vacant upon the elevation of LeRoy F. Millette Jr. to the Court of Appeals. Alston was elevated to the Virginia Court of Appeals in 2009 to fill the vacancy created upon the retirement of Jean Harrison Clements.
In 2018, President Trump announced his intent to nominate Alston to serve as a United States District Judge of the United States District Court for the Eastern District of Virginia. He received his judicial commission on June 12, 2019.