Do you mean that you want to install Jira on an existing web server or Java container? For example, you have already Tomcat installed and you want to add Jira there? If so, then from Jira 7.0 Atlassian stopped releasing war distributions.
You can read more here about it
If by "web server", you mean "another computer that runs as a server", there is no difference in installing. Whereever you install Jira, it runs as a service. If you're planning to make it available to lots of people on that server, you may want to think about using a proper name and getting rid of the port numbers so that other users see it as part of your web site.
If you do mean "run it on my own Tomcat/Glassfish/Websphere/etc", then mark Alexey right - you really don't want to try to do that because you'd have to extract it all from an install, and it's not fun (or stable, or supported)
@Jack Graves [AC] first caught our eye with his incredible breakdown of what, in his opinion, can make or break a Jira software implementation. (Read his thoughts on this thread)! In this follow...
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