Running a servlet in Weblogic 7.0 involves the std process of writing a servlet class and web.xml Deployment Descriptor(DD) in a standard war style packaging. You also need an additional DD called welogic.xml where you should at least specify the context-root. For eg, to access your servlet at
http://server ort/mywebapp you should set the context root to /mywebapp. This is different from tomcat (in case you are used to it) where the context root gets decided by the folder name. Weblogic Builder is a great tool for creating DD and deployment. You can also try hot deploying your apps by putting them in the "application" directory.