The nearest airport is the Kullu Airport which is located at a distance of 50 km from Manali. From the airport, you can take taki a cab to the nearby bus stand and then take a bus to reach Manali which will take about 2-3 hours.
There are several private and state buses which you can get to Manali. Usually, it takes around 14 hours to reach Manali from Delhi and around 8-9 hours from Chandigarh.
You can get discounted Volvo bus tickets on websites like Redbus, Goibibo, etc. so make sure you check them out. The state buses for Manali start from 777 INR from Delhi and can turn out to be a little uncomfortable and chilly during the winters.
Also, you have the option of driving to Manali but make sure that you start early morning to avoid driving at night time through the hills.
The nearest railway to Manali is Ambala Cantt. which is connected to several major places like Delhi, Chandigarh, Haryana, etc.
So, you take a train till Ambala Cantt. and then take a state bus to Manali which will take about 8-9 hours from here.