The primary Red Line includes the big stuff for visitors, from the airport through much of the business locations and on out to the Mall of the Emirates (the one with the ski slope).
The horseshoe Green Line fills in some gaps.
There are Gold VIP cars that cost a bit more, and are a good option with luggage during rush hours.
The only downside for airport passengers is the Metro shuts down during the middle of the night, when many flights arrive. Check hours in advance as they occasionally change.
And the one thing it cannot do, is avoid the rotisserie effect of walking in Dubai’s heat between the station and your destination.