By road. If you want to go on a road trip then reach Chandigarh by local transport and then start your road trip, otherwise there are many options for bus and they are pocket friendly too.
Yes all said bus is good option hrtc himsuta but thia peak season for tourists to reach all over the himachal. so might be you got stuck at there where you could not find a good cheaper and best way to roam around. The taxids taking too much of money to travel even 5 km. Best options is bike and second your own car. taking less time can enjoy beauty of my state at ang time anywhere
Travelling by road would be the best mode. Buses are available from Delhi to Manali - from Majnu ka Tila, Kashmere Gate, ISBT etc. It would be a 10-11 hours journey approx. Good luck!