If you can add HTML, you can embed appointment scheduling into your website. For Joomla there is a good reference at http://support.powerdnn.com/KB/a50/how-to-add-html-code-into-a-joomla-article.aspx covering different ways to add HTML into Joomla.
The code that you'll need to add to your site is available in your Client's Scheduling Page section.
If you'd like Acuity to embed your scheduling page into a personal website, we're here to help! Head to the Client's Scheduling Page section and select "Embed the Scheduler for Me" to request the scheduler embed.