Once you install the Mendeley Desktop App it will give you the option to import your current EndNote citations.
If this feature doesn't work, the process for doing this manually is listed below.
To import your EndNote library, you need to first export your references to an 'EndNote XML' file and then import that into Mendeley Desktop
In addition to the EndNote XML format, you can also export references to Bibtex and RIS format in EndNote which Mendeley Desktop can also import. In EndNote select Edit > Output Styles > Open Style Manager. Check the 'Bibtex Export' and 'RefMan (RIS) Export' options in the list that appears then close the window. Then go to File > Export... and select the 'Text File' type. In the box labeled Output Style, select either Bibtex Export or 'RefMan (RIS) Export'. In the filename field, enter a name ending in ".bib" for Bibtex or ".ris" for RIS export and click 'Save'.