Problem Statement
It may be possible that sometime you need to code or provide a link to directly download a report.

Solution
In order to directly export a report, navigate to following URL. This URL request will prompt you with open/save dialog to export the report.

ExportReport

Here,

https://na1.salesforce.com is Salesforce hostname on which the org is hosted
00O30000001Y9ll is report Salesforce ID
export=1 is the parameter required to request system for direct download of report

Also note that,

Salesforce out of box feature does allow exporting of report, but its 3 step process
Navigate to report
Click Export Details
Click Export