Harpreet, what you're asking for is just impossible to do natively. You just have to shoehorn what you want sometimes into JIRA.
You might consider creating a special issue type called "Sprint Goal" and then associating it with each sprint. That could be messy, but functional. In general, there's no way to provide metadata about a Sprint in JIRA because it's never really exposed to the user except through the UI artifacts in JIRA Agile.
Your original question says adding a note for the Sprint.
If you are looking at a Story level, of course you can add a custom field.
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Design notes for a Sprint? If you are looking at having some common guidelines for Sprint, use a confluence page for it, while I also would have preferred as place in JIRA Agile (a.k.a GreenHopper) itself to put down common information about sprint like Sprint Goal.
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