Style.css not taking changes

also, please post a live link to your site to illustrate the problem, and explain which formatting you are trying to change.

I am doing it on my system…is there a possibility that I can first migrate my website (I mean upload the word press back up of my site to godaddy)…

That can be done, but I have never done that and some folks have difficulty with it. Do you already have content (pages, posts, etc.) in your database, and uploads in your wp-content folder? Depending upon what you already have, you might or might not need this:
http://codex.wordpress.org/Moving_WordPress

…and then do editing from go daddy only.

I have a different host, but that is how I do things.

How will I do that?

I use FileZilla and an SFTP conntection:

http://support.godaddy.com/help/article/104/connecting-to-your-hosting-account-with-filezilla-ftp

note: If/when you might set that up, ask them whether you can make an SFTP connection since FTP sends and receives your server login credentials in plain text.