So, now, we’re moving over to SharePoint PowerShell, right. Formerly, we used STSADM from a command prompt. Therefore, here are the old and new commands for solution management, to do the following:
Add a Solution
Deploy a Solution
Retract a Solution
Delete a Solution

The STSAdm commands were:
Add Solution:

stsadm –o addsolution –filename D:\YourPath\YourSolutionName.wsp

Deploy Solution:

stsadm –o deploysolution –name YourSolutionName.wsp –url http://YourWebApp –immediate

PowerShell commands:
Add Solution:

add-SPSolution D:\YourPath\YourSolutionName.wsp

Deploy Solution:

Install-SPSolution YourSolutionName.wsp –WebApplication http://YourWebApp 

And, naturally, if your solution is installing a DLL (to the GAC), you would need to add the following attribute:

-GacDeployment

For Retracting and Deleting, the STSAdm commands were:
Retract a Solution:

stsadm –o retractsolution –name YourSolutionName.wsp -url http://YourWebApp -immediate

Delete aSolution:

stsadm –o deletesolution –name YourSolutionName.wsp

PowerShell commands:
Retract Solution:

Uninstall-SPSolution -Identity YourSolutionName.wsp -WebApplication http://YourWebApp

Delete Solution:

Remove-SPSolution -Identity YourSolutionName.wsp