Bus

Mandi town has an Inter State Bus Terminal, which has frequent buses from New Delhi, Chandigarh, Shimla, etc.
HRTC has a good service in Himachal Pradesh with Himsuta's and Himgauarv's as the recommended mode of travel.

You can choose to book HRTC buses from this link.

Train

The nearest and most approachable railway stations are Kiratpur Sahib and Chandigarh. From these locations, one can take a bus or hire a taxi.

Air Travel

There are airports at Chandigarh, Kullu and Dharamsala. From these locations, one can take a bus or hire a taxi.

For Mandi town to IIT Mandi, you can choose to hire a taxi or board an IIT Mandi bus, here is the link for the institute bus schedule.