After purchasing the DLC and loading up your game travel/fast travel to any festival HQ and enter the autoshow or alternatively press
and head into the 'Porsche' menu and choose the 'Porsche Autoshow' and then choose your car from there.
All DLC cars are free the first time you buy them so simply choose from any of the 10 new Porsches:
1970 Porsche 914/6
1982 Porsche 911 Turbo 3.3
1987 Porsche 959
1989 Porsche 944 Turbo
2003 Porsche Carrera GT
2012 Porsche 911 GT3 RS 4.0 (997)
2014 Porsche 911 Turbo S
2014 Porsche 918 Spyder
2015 Porsche Cayman GTS
2015 Porsche Macan Turbo
Once 'bought' the achievement is yours.