You need to get a dump of the database, this can be done through phpMyAdmin.
To backup the site, you need the database, and a copy of the file tree. Or just the modified files at least. plus some special directories like img/wiki_up.
Its probably best if you copyed the whole tree just to make sure.
To install then, just upload the tree somewhere and import the database. Some hosting providers TikiFriendlyHosts will do the whole process for you