I am very novice to this share and investment things. Recently, the news is flooded in internet with "twitter plans its share sale". I am thinking, we as international student can also buy some share. It doesn't mean i have lot of money just thinking if i can use my some savings.

Yes, International students can buy shares. You are also obligated to pay taxes on the income from the shares.

As for Twtr, the IPO is set for Nov 7th. Unless you have a big brokerage firm account IPOs aren't accessible for novice traders and general public. However once it starts trading in the market you can immediately purchase the stock so be in a lookout as soon as IPO is released. Looking at FB, Twitter should do well in short to mid term range.