NuGet tools require that sensitive operations such as push and delete are authenticated with the server using an apikey. The API key you should use is in the form of username:password, where the password can be either clear-text or encrypted.
Set your API key using the NuGet Command Line Interface:
nuget setapikey admin:password -Source Artifactory
Now you can perform operations against the newly added server. For example:
nuget list -Source Artifactory nuget install log4net -Source Artifactory