no u dont have to have a domain .. i think.. you have to have a good server.. with mysql
just get hostmoster hosting or from any of those sites
if u have already done that just follow the rest of the steps below.
i am guessing that u have checked the joomla help i'll tell u what i do.
ok so first you have to make sure that u have a server with my sql installed in. the best thing to do is get space at some hosting website.. cuz you get everything php, mysql, ftp, etc...
when u have that space with mysql installed you need to make a user in my sql (I dont know much about sql usually i use host-monster or host-gator's mysql automatic creation wizard)
then when you download the joomla its in a zip folder... unzip that to a folder and then copy your zip joomla1.5.zip in that folder as well with all the files.
upload that to the root of your server, then just open your site and begin the installation.
when u get to my sql part (the worst part ever to deal with) type in the user that u have created with ur mysql wizard with the password joomla will create all the tables in the my sql database..
after that its just simple just keep on clicking next lol n make sure u install the sample data that helps a lot if ur a beginner.
n thats pretty much it pm me if u need more help