Turin and Milan airports are the most convenient, respectively one hour and two hour drives.
From Turin options are:

from Turin go to Carmagnola and Bra, and continue in the direction of Pollenzo and La Morra
on the motorway A6 Torino-Savona, exit Marene and continue in the direction of Cherasco and La Morra (SP 58)

From Milan or from Southern Italy, via Genova, follow the motorway A7 exit Tortona, take the motorway A21, exit Asti Est, continue in the direction of Alba and Barolo – La Morra.
Or you can take the motorway A26 from Genova Voltri, exit Asti Est, continue in the direction of Alba and Barolo – La Morra.