jdbc:jtds:sqlserver://x.x.x.x/database
replacing x.x.x.x
with the IP or hostname of your SQL Server machine.
jdbc:jtds:sqlserver://MYPC/Blog;instance=SQLEXPRESS
or
jdbc:jtds:sqlserver://MYPC:1433/Blog;instance=SQLEXPRESS
If you are wanting to set the username and password in the connection string too instead of against a connection object separately:
jdbc:jtds:sqlserver://MYPC/Blog;instance=SQLEXPRESS;user=foo;password=bar
(Updated my incorrect information and add reference to the instance syntax)