Often site owners think that their site is HUGE and that must be part of the problem. Generally, that is not the case. MySQL is capable of handling tables with many hundreds of thousands of records without much effort so the chances that your site is slow because you have thousands of items is pretty unlikely. There are other much more likely culprits that you should look at before you start messing with your Joomla database.
Problem #1: Hosting Environment
Probably the most common issue making any site slow is the hosting service. If you are on a shared server, there are a few things you should understand. First, your site is one of many on the server. Probably hundreds if not thousands of sites are usually put on a single shared server. The budget hosting companies are notorious for having many thousands of clients on a single server.
Second, shared servers are not configured for optimal performance. They are configured to be easy to admininster and to be as secure as possible to protect the many clients on a single server. Since it would be nearly impossible for a hosting company to police the quality of the code and the version of software users are installing, they tend to lock down as much as possible to help mitigate the security risk of having many users.
Solution: Quality Hosting
We recommend hosting your site with a reputable provider that specializes in Joomla. RochenHost.com, CloudAccess.net, and Liquidweb.com are pretty safe bets. These companies have experience with Joomla and their servers are configured to run Joomla and other CMSs more efficiently.
If you are making money with your website or your site is mission critical, then you should definitely be looking at a Managed Virtual Server or Dedicated Server to insure your site is not hampered by other users on a server. This is the only way to guarantee that there won't be a user jamming up server resources with bad scripts or that the server simply won't be overloaded due to the number of users. Cloud hosting is also a good solution as you can purchase an much or a little hosting power as needed for your site to run fast. It is generally very easy to allocate more resources should you suddenly need more as well.
Problem #2: Site overhead
Solution: Optimize website assets
Another easy way to reduce the amount of data transfer is to use gzip compression. Gzip is a combination of your web server using gzip compression on the files it sends to the user's browser. The browser then decompresses the files once they are downloaded, saving some of the data overhead of uncompressed files. All modern browsers support gzip so there's really no reason not to enable it on your site.
Problem #3: Network Latency
Many people don't realize the impact network latency can make on the time it takes to download a page. Latency is slowdowns in the data flow from the server to the browser. When a user requests a web page, there are actually many requests taking place based on what is on the page requested. It is not unusual for a single page to have 100 or more requests. There are many factors that can affect the data flow, many of which are out of a site owner's control. One factor that can be controlled however is routing latency. When information is being transmitted from one internet router to the next, each hop adds a little bit if latency. Also, the type of connection, be it fiber, copper, or coax will also affect the amount of latency. The longer the distance from the user and the more hops the data has to make, the more latency the user will experience. When a page on a site requires over 100 requests, even 50 ms per request can add up to a noticeable amount of time for the user.
Solution: Content Distribution Networks
Content distribution networks (CDN) allow a user to receive all of part of the website they are requesting to be served to them by a server that is physically closer to them. Rather than a user from Thailand waiting for a site in London to make the long journey, the site would be served from a web server in Bangkok, reducing the amount of latency the user would experience. There are several Joomla extensions that help site owners implement CDN technology from Amazon Cloudfront, MaxCDN, and other networks. This is particularly important if your site serves an international audience.
Out of the box, a basic Joomla install will be pretty fast. If yours is not, then these are 3 surefire ways to help increase the speed of your site.