The assumption is that you have already received an offer letter for internship in Switzerland :P
All facts mentioned are of the period when I went to intern. They might have changed. So here goes.
The major Swiss Universities are EPFL and ETH Zurich for IIT students.
If you plan early enough, you can actually manage to get Swiss Air return tickets as the cheapest options.
There is a flight daily from Mumbai to Zurich. From Zurich, it is best to take a train to your destination city. I made the mistake of taking a flight from Zurich to Geneva and then a train to Lausanne.
The trains in Switzerland are run by SBB. The first thing to do after getting your luggage from the airport is to buy a SBB Half fare card. Valid for a year, it reduces all your tickets to half the price. If you are going to do even the slight amount of traveling, you will recover its cost very very soon. Trust me on this one. And if you are even a little adventurous and an evening traveler, the Track 7 card will prove to be really useful too. I highly recommend it. To buy these at the station, you have to ask at a CFF (railway) desk. Keep your Swiss address and passport pictures handy along with cash.
Find all the information you need on SBB site. You are going to be seeing a lot of this website.
Local Transport in Lausanne
Buying a monthly pass for 41 francs is advisable. It covers both metro and buses. You can get that made from the SBB counter at EPFL or at Lausanne Flon. Otherwise, each normal journey costs 2 francs with half fare card.
Luckily, I was picked up from railway station on my first day. Otherwise, normally there is some problem to manage all that luggage and finding your way about in the a new country.
Among the 6 student accommodations, Bourdonnette (where I stayed), part of Cedres and Ochettes have apartment systems. Rhodanie and Falaises are more like a dorm. All of them have some advantages and disadvantages. Bourdonnette worked really really well for me.
Your first 10-15 days might be cold. So take some warm clothes. Especially, if you are not from North India and used to some amount of cold. If possible, take something for the night. Bedsheets, pillows and all are not included in your room rent. Though you can take them from your house manager for around 50 francs which is not so bad.
If you are not staying in an apartment, do take cooking utensils and food from India else you might have to buy there and that is not cheap.
Take atleast 500 francs from India for your initial expenditure including Half fare card.
Shopping and Food
All shopping is done at Migros and Denner supermarkets. Migros is the cheapest. Denner is cheaper for some things. The most important thing: Migros doesn't have Alcohol and cigarettes. Denner \m/
Shops in Switzerland usually close at 6:30 or 7 pm. Even earlier on Saturday and on Sunday everything is closed. Migros at Ouchy is an exception.
There are also Indian shops close to Avenue de France and one under Lausanne station.
Do take health insurance from India with large remuneration. Around 100 000 USD upwards.
Post questions in comments.
More travel and living advice later. Have fun in Europe.