There is a frequent service of buses, taxis, coaches from Delhi and Chandigarh to Kasauli. If you want to drive from Delhi, follow the NH 1 to Ambala crossing Sonepat and Karnal. From Ambala take NH 22 to get to Kasauli. En route you will pass through the cities of Panchkula, Zirakpur, Pinjore, Dharampur and Parwanoo. There is a narrow hill route from Dharampur that leads to Kasauli. An alternative hill route is also there from Parwanoo which leads to Kasauli via Manoan, Jangeshu and Mashobra. Note that the Parwanoo route was a part of old India and is now the Tibet road, under The Heritage Protection Act. Also keep in mind that there are no fuel stations anywhere in Kasauli, the closest one is 12 km away so it is advisable to be prepared if choosing to drive here.
Nearest railhead is Kalka in Haryana, which is 40-km from Kasauli and 44-km from Solan. Solan is also connected with narrow gauge railway line from Kalka.