Rent a bike from Delhi and enjoy the scenic view of amazing Himachal. if not then take a volvo from Majnu ka Tila ( Delhi ).Book your volvo in advance through any online portal.
If you want an economical trip so travel by train upto Chandigarh and then take HRTC's ordinary bus from Chandigarh to manali.
I would suggest you to stay in gurudwara which is in kullu it is the cheapest way to stay for a night and then in morning u can head towards manali .
If you'd like a comfortable journey, go via bus. From Delhi, you can board buses from ISBIT, Kashmere Gate or Majnu ka Tila. If you'd rather go by bike, It would take around 10 hours to reach Manali.
Take a bus from Delhi which are always there in kashmiri gate or majnu ka tila or you want to travel more then go by train to Shimla ND take Himachal Pradesh public transport to Manali and if you want to drive by yourself and you have a nice budget then hire a car for the trip because bikes might sound cool and all but it gives a back pain as well
Best and convinent way is to travel by bus and after reaching there hire a bike to roam around. But before going please do check if Rohtang pass is open.