Installing Joomla on a local web server
From Joomla! Documentation
Note: This tutorials is targeted for non-expert audience, if you need more detailed and advanced information go to the Developers page.
Fist thing to do is to check if your web server meets the Joomla technical requirements, visits this page so see the Joomla requirements table.
If you are not a tech person, the easiest way to check if Joomla is compatible with the server you own is to mail the support guys of your hosting company with something like this.
Good day sirs I would like to know if the server I rented is capable of run a Joomla installation smoothly, this is the Joomla Requirement page: http://www.joomla.org/technical-requirements.html Thanks for your help, have a nice day
Event the cheapest web host providers normally answer this kind of support questions in less than 3 hours, so relax and wait for the answer.
Now if you are a computer enthusiast and you got in your personal computer a local web server using XAMP, LAMPP or any other and this server is up to date, you can be 99% sure Joomla will run just fine on it just give it a try to see yourself.
Installation on rented servers
There is several ways to install a Joomla copy on a rented web server but the methods and procedures may vary depending on the server provider it configurations and limitations, for example, some web server providers give you the option to do the famous "one click install" it consist on press a button and your web server provider will run an automated script to install a copy of Joomla in your rented web server, if you have hard time finding this options just send a mail to the support guys of your server provider with something like this:
Good day sirs I would like to know if your guys have the "one click install" option to automatically install a pre-configured copy of Joomla in the server I rented. Thanks for your help, have a nice day.
As mentioned before some web server providers have this option and others not, and be aware that some lazy web server providers may have a one click installation option BUT... using a very old and outdated Joomla version.
Having this clear let's say you want to install a Joomla copy manually on your rented web server, if so