Start SharePoint 2010 Management Shell (As Administrator) and run the following
Add-SPSolution –LiteralPath C:\WebPart\packagedwebpart.wsp
then you can do this:
Install-SPSolution –Identity packagedwebpart.wsp –WebApplication http://sp2010 -GACDeployment
or this:
In Central Admin, click on System Settings > Manage farm solutions to see the web part. Click on it and select Deploy to deploy it.
Depending on how the wsp has been created, you may need to enable the web part in the site collection features.