Depending on where you got a custom webpart from, or what it even does, the instructions to install it are not always clear.  In such scenarios, the following 2 commands may be useful to you.

Note:  Run these powershell commands from the location where your webpart is located.

stsadm -o addsolution -filename webpartname.wsp

Update-SPSolution –Identity webpartname.wsp –LiteralPath C:\temp\webpartname.wsp –GACDeployment