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Different approaches can be used to increase the time your website is displayed on your users computers.
You can measure the time it takes for your page to load with Firebug, an extension for Firefox. Once downloaded, installed, Firefox restarted (use the brain hack to keep open Tabs), you will find a small icon in the lower right area of your browser. Click enable, if it asks, then you can start viewing your page using the “Net” -tab (all) of Firebug. It will tell you how long the page took for loading. You will be surprised by the wide spectrum of details you will get to know about your website. E.g. using fat script libraries such as (full) scriptaculous or prototype take quite some time to load. Often whole libraries are included for effects that only need a handful of functions (lightbox!). More under a.4 later on.

a. reduce the over-all size of files/data that will be transfered when accessing your site

   a.1 images (jpg/png/gif)
   a.2 markup (php/html/css)
   a.3 stylecheets (css)
   a.4 javascript (js)
   a.4.1 overview of different lightweight javascript libraries/frameworks
   a.5 general (plugins, temporarily removing 'fat files')

a.1 Save bandwidth and optimize speed reducing images (jpg/png/gif)

Many websites use a high amounts of images, and there is nothing bad about it,
as long as a suitable compression is used. There is a difference between images compressed with jpg (jpeg), png and gif.
While jpg is great for images that feature loads of different colours, gradients and generally speaking pictures (photos), png and gif make more sense if an image does only consist of few different colours (max. 256 for good results). Gif images have to be used if you are going for transparent or semi transparent images. PNG can be transparent as well, but there are issues with the Internet Explorer, so I’d not recommend using png for transparent images. A jpg compression of 60 is often far enough, no need to go by even higher, because most of your users will most likely not see any difference. The difference file size concerned is massive.
You can easily safe some kilobytes there. REMEMBER: less kb to download = faster display of site. Safing photos in gif or png file format makes them ugly and big, so stick to jpg.

a.2 Save bandwidth and optimize speed using valid markup (php/html/css)

While this seems to be hard for many designers and programmers, one should try to produce valid markup.
Valid markup displays faster on many computers. Don’t over comment your source on websites.
It might be a good idea to keep local commented copies of your files, but in the web that’s only resource and thus speed hogging.

I’d recommend this online HTML tidy program for checking your markup, as well as the official w3c markup validation service [For CSS]
A great online tool to strip comments from your code (html/js) is memtronic’s packer
as well as dean edward’s packer.

a.3 Save bandwidth and optimize speed using compressed CSS

Compressed CSS is loaded like ordinary CSS, but simply faster. REMEMBER: less filesize = less load time of page
If your pages’ CSS is loaded faster, the site is earlier displayed on your visitors’ PC. He/she is then more likely to not leave your page in the first 10 seconds if he/she sees the content. It is essential to aim for the below 10 seconds (check the time your users remain on your website with Google analytics). There are some CSS compressors that work and others that proclaim they work, but don’t. Here are three, that definately work more or less depending on the complexity of coding.

CSS compressors
Flump cake css optimiser
icey’s css compressor
css formatter and optimser

a.4 Save bandwidth and optimize speed using compressed js

Many WordPress scripts want you to include big and fat javascript on your blog. Usually those can be compressed, downsized and optimized. I mentioned two compressors before: memtronic’s packer
and dean edward’s packer.
A by far even better compressor is dojo shrinksafe.
You can use these compressors to remove descriptive lines, comments and examples from the source. Usually compressed files will still work. If they don’t, use another option or different compressor. Be sure to compress valid js markup only.

a.4.1 Overview of javascript libraries and compress JS

So basically we all know scriptaculous and prototype. Some also know mootools (and moo.fx), but my personal #1 is byte.fx with an overall size of 3kb.
Prototype and scriptaculous can be compressed to some extent, Steve Kallestad did that and offers these compressed files on his site:

The downloads are available at:

• Prototype.js 1.50rc1(25K as is, 13K with gzip compression, 64K uncompressed)
• scriptaculous 1.65 (41K as is, 20K with gzip compression, 105K uncompressed)
• combined prototype and scriptaculous (62K as is, 29K with gzip compression, 169K uncompressed)

Be sure to check them locally before you take these versions for an online test-walk!

a.5 Save bandwidth and optimize speed deactivating or tweaking plugins

Many wordpress plugins are filled with explanations, comments and examples.
These can be removed to save additional space and thus increase the download speed of your website.
Use the mentioned above compressors to compress plugins like Lightbox or Flash-embedding plugins.
If you ever run low on bandwidth, deactivate unneeded plugins (and later on re-activate them!) for the needed time.
You will be surprised by the amount of traffic the lightbox.js does generate.
Also check your site for deadlinks, sometimes a deadlink generates a 404-error page. If you got custom error-pages that render a nice “not found”-page, this is a massive traffic and bandwidth generator. Locating these files and fixing their deadlinks is essential to maintaining a slick site.

b. enable server-side options to tweak the way stuff gets transfered

  b.1 gzip compression
  b.2 *Sql tweaks / WordPress 2.1

b.1 Save bandwidth and optimize speed using server-side options

If you can get your hoster or admin to enable mod_deflate (former mod_gzip), you are most likely to save tons of bandwidth, because of serving compressed content. Note: not all browsers support this. Read all full tutorial on that here.

b.2 Save bandwidth and optimize speed using sql-tweaks (WP 2.1)

In January this year, WordPress 2.1 was released:
They state:
[...] Much more efficient database code, faster than previous versions. Domas Mituzas from MySQL went over all our queries with a fine-toothed comb [...]
But if you want some real fast WordPress a-like CMS, go for Flatpress, a SQL-less CMS (currently under development). Static files, such as html, load faster than any dynamic ones. just as a golden rule.

c. move the server to a location where most of your visitors come from

  c.1 mirrors and foreign hosting

c.1 Relocating your website

Sometimes it makes more sense relocating your website to the country of #1 traffic origin or offering a mirror server then merely tweaking your site. If you’d for example have a Fansite dealing with an American (US) actress or model, but run your website from Europe, then most of your targeted audience (Americans) will have a slower site experience than if you’d place a server on the American mainland. Even ‘mainland’ is not equal mainland, due to the huge geographic distance of the east and westcoast. Thus offering mirror might be a wise idea. So based on the origin of site request either www1 or www2 is accessed.