Connecting to database using Toad in windows
It's not clear from your question what brand of database you are connecting to.  I will assume it's Oracle.
You need this information:


name of the server the database is on
name of the database  --sometimes called a service name
is the database parameter db_domain configured with a value?  (usually the domain name)
the port the database listener is using (usually port 1521)
a user and password, be good and don't connect as sys


Let's try the easiest way, connecting directly


open toad
select session/new connection from the menu
select the "Direct" tab from the right side and enter

User and password
Host = machine name of the database server
Port = 1521
Service Name = Name of the database

connect as normal if you are not connecting as sys
ensure that the Installed clients picks up the correct install of your Oracle client


and....press connect.

This is the easiest way.  More involved is adding the name of the database to the TNSNames in your oracle client.
Another good check is to log onto the server where the database is and start a DOS command line window.  Enter lsnrctl status  .  This will give you the database name and port and if the listener is ready to receive connections.