Dallas/Fort Worth International Airport: For Downtown, take DART’s Orange Line from DFW Airport Station (by Terminal A) to West End/Union Station/Akard: roughly 50–60 minutes and about $3 for a 3-hour pass, or $6 for a day pass. It is far better value than a $35–65 rideshare if you are staying downtown, Uptown, Deep Ellum or near rail. For Fort Worth instead, take TEXRail from Terminal B to Fort Worth Central Station (about an hour; fares start around $2.50).
Dallas Love Field: There is no rail station at the terminal. Take DART Love Link bus 524 to Inwood/Love Field Station, then the Green or Orange Line toward downtown; allow roughly 30–45 minutes total and use the same roughly $3/3-hour or $6/day DART fare. A rideshare is sensible here if you have heavy luggage or are staying outside the rail corridor: Love Field is much closer to central Dallas than DFW.
Dallas Union Station: Amtrak’s Texas Eagle calls here, as does the Trinity Railway Express (TRE) from Fort Worth. Union Station is directly on DART light rail and walkable to Dealey Plaza; use it as your base transfer point. Do not build a tight itinerary around long-distance Amtrak arrival times: freight delays can be substantial.