To run multiple websites on a single Linux VPS, utilize virtual hosts. Begin by creating directories for each site and setting permissions. Install Apache if not present and create distinct virtual host configuration files for each website. Customize these files with server details and directory paths. Enable virtual hosts, restart Apache, and ensure DNS records point to your VPS IP addresses. Populate website directories with content and test each site by navigating to its domain. This approach optimizes resource utilization, allowing you to efficiently host and manage multiple websites on a single Linux VPS server.