DART (Dallas Area Rapid Transit) trains run every 20 minutes. Akard Station is a 5-7 minute walk from the Magnolia Hotel. The time to and from Love Field (DAL) is 30-35 minutes, and to and from Dallas/Fort Worth (DFW) is about an hour. Lyft or Uber could cut that time almost in half, but only if traffic is light, and it is much more expensive. A DART ticket costs $2.50.
At DFW, DART trains arrive near Gate A10 on the lower level. If you're not checking bags, it's fastest to go through Terminal A security and take the internal Skylink train (every 2 minutes, upstairs to the right outside security). If you're checking bags and don't leave from Terminal A, take the Terminal Link shuttle (Orange bus, every 10 minutes outside baggage claim upper level near A10).