I have to visit Munich, Germany for a couple of weeks this month for business purpose. I am absolutely ignorant about German language. Although I won't be interacting with the locals much, I'll have to use the public transport. How problematic can it get? In India, most of the sign boards are written in English as well. How is it in Germany? Is there any way I can learn few German sentences and words to get around the city?
Not very severe. In Munich as with most of Germany, automated transport ticket machines can be changed easily to a number of different languages. Physical German signs are mostly in German but their alphabet is very similar to English so can be easily memorised when you need to know certain place names. However, Munich is a very walkable city which I would recommend doing if you are very central.
I would recommend getting a phrase book so you can grasp the very basic of the German language (Hello, Thank You, Good-bye). Although the majority of touristy places speak very good English it is courteous in Europe to at least try with the local lingo. They would appreciate it greatly. The German language is very phonetic with the emphasis usually applying to the first syllable in a word.
You'll be fine. Especially young people or people in tourism-related jobs speak good English. Public transport is well-organized and easy to navigate.
It might help you to plan your trips and tickets ahead of time (i.e. where you are changing subway lines and what ticket you need - they have a rather complicated zones system so you might just want to get a weekly/monthly ticket for the central area once you're in town). Announcements on some subway lines are bilingual in German/English but in general you can just read the station names off the wall in stations and compare to a line map to see when you have to get off the subway. Also when arriving at the airport there is English-speaking staff where you buy the tickets that is able to assist you and so will be your hotel/employer/friendly strangers.
You asked for German sentences. In case you are not confident in your German pronunciation I would rather go for few but well practised phrases than many sentences:
Your most important sentence next to "Hallo" and "danke" should be "Sprechen Sie Englisch?"
As others already have said, a lot of people speak good English in Germany - especially in large cities like Munich. As a native I really prefer someone speaking understandable English over someone trying to speak German, because of courtesy, but me not understanding a thing.
If you still need more (i.e. asking directions), prepare a notebook where you write down the sentences and show them to the people. You would be surprised how far you come with just making signs with hands and feet.
My experience in Munich included many conversations like this:
Me: "Ja, ein großes weißwurst und ein schwarzes Bier, bitte."
Wurstmeister: "Would you like mustard and relish on your sausage?"
My German friends (all of whom speak better English than some of my Canadian friends) are of the opinion that if the person has tried to learn even a little bit of the local language and custom they are happy to switch to English. If the tourist has the attitude of "everyone MUST speak English" then they kann diesen Touristen nicht heute verstehen.
So, get a german phrasebook at the airport bookstore, or a basic german lesson from iTunes. Couple of dozen phrases and numbers under 100 should be more than enough, and it's something to do on the plane.