In linked servers - you'll need to make sure you have permissions on both servers that you're looking to set the link between.
So for instance - if you're sa on Server A, you'll still need at least read-only access to the database you're trying to access on Server B in order to use the linked server.
Additionally - when you're configuring your linked server, it's important to make sure your security context is set correctly.
By default, Linked Servers are made without any security context which puts the responsibility for authentication on the connection string you specify.
Usually you'll want to use the credentials of who is attempting to connect through the linked server by selecting "Connections will be made using the login's security context", but this varies based on you and your companies needs.
More information on linked servers can be found on technet:
General Linked Servers -
Linked Server Security -