The "correct procedure in deploying" is to manually copy the WAR or EAR file to the server/xxx/deploy directory.
In Eclipse, you will want to make certain that the EAR or WAR project is associated with the server. To do this, in the Server View, right-click on the server and select Add and Remove. In the Add and Remove dialog box, select your project in the Available list and click Add to move it to the Configured list and then click Finish. Then you might also have to right-click on the server and select Publish. You can do the above steps with the server running or stopped. If the server is running, so is your app.
