How do I query my linked server records in MS SQL 2000 Server?

Querying the tables is dependent on what the driver expects:

but you can try select * from swdate...<tablename>

or select * from openquery(swdata, '<text of query>')

Do this in Query Analyzer

you query the linked server by fully referenceing it...

select * from swdata.dbname.owner.tablename

Trying any of the queries above I get this error:
Server: Msg 7202, Level 11, State 2, Line 1
Could not find server 'SWDATA' in sysservers. Execute sp_addlinkedserver to add the server to sysservers.

How would I execute this with the right syntax?

Syntax
sp_addlinkedserver [ @server = ] 'server'
    [ , [ @srvproduct = ] 'product_name' ]
    [ , [ @provider = ] 'provider_name' ]
    [ , [ @datasrc = ] 'data_source' ]
    [ , [ @location = ] 'location' ]
    [ , [ @provstr = ] 'provider_string' ]
    [ , [ @catalog = ] 'catalog' ]

" Trying any of the queries above I get this error:
Server: Msg 7202, Level 11, State 2, Line 1
Could not find server 'SWDATA' in sysservers. Execute sp_addlinkedserver to add the server to sysservers."

If you are getting the above error, then your linked servers are not set up correctly or the SQL Login that you created for the linked server doesn't have the proper rights.  The user will need to have rights on both servers in order for the link between servers to work properly and it should probably be the same user on both server.  

As for querying a linked server, QPR has it right.  You need to fully qualify the server name in order to query it.

Hope this helps,

Pete J.