Try something like this. Running it with the -WhatIf will only report what would be deleted by this command. Remove the -WhatIf when you're ready for it to do work.

#################################################

#init variables

$directory = "\\servername\sharename"

$retentionDate = (Get-Date).AddDays(-2)

#################################################

# nothing below here needs to change

Get-ChildItem $directory |? {($_.PSIsContainer -eq $false) -and ($_.LastWriteTime -lt $retentionDate)} | Remove-Item -WhatIf

Add -Recurse to the Get-ChildItem call to also delete old files from sub-directories:

#################################################

#init variables

$directory = "\\servername\sharename"

$retentionDate = (Get-Date).AddDays(-2)

#################################################

# nothing below here needs to change

Get-ChildItem $directory -Recurse |? {($_.PSIsContainer -eq $false) -and ($_.LastWriteTime -lt $retentionDate)} | Remove-Item -WhatIf