best places to visit in Czech republic.what is the best season to visit?proceedure for visa?

I have no idea how a person from India would get a visa,try contacting the Czech republic Embassy in India or indeed a lawyer who specialises in Visas.

Prague, Karjstein Castle, Cesky Krumlov. August 2014 was sunny, warm and dry but maybe I was lucky.

And Hradec Kralove, Olomouc, Kromeriz, Brno, Telc, Litomerice, Frantiskovy Lazne, Tabor, Ceske Budejovice...
Get yourself a guide book and look what appeals to your taste and interests.

Outside of Prague I recommend these places: Brno, Plzen, Hradec Kralove, Olomouc (Olmütz) among others.

All necessary information about tourist visa to the Czech Republic you can find here:
http://www.vfsglobal.com/czechrepublic/India/
What are the best places to visit? Well, most first time visitors to C.R. go to Prague and Cesky Krumlov. Then it depends for how long you will visit, what you like and what you are interested in. One of the best source of information for shorter visit is Rick Steves book: Prague & the Czech Republic and I would add Brno and Marianske Lazne which are not in the book.
Which is the best season to visit? It depends: if you want to do some skiing then winter. If you are more into outdoor swimming I would recommend summer. For travel and walks around I think the best are late spring and early fall. Not too hot, not too cold. If you tell us for how long you are visiting and what your interests are I could be more specific.