Surprisingly it's come on a huge amount, both browsers and phone's data transfer capacities have improved massively, as has the price of bandwidth.
Step 1: Connectivity.
Next up you have the plethora of connections in the sky, edge, 3g, gprs, 3.5g and so on, check your phone's native settings, though it might be capable of better communication you might have to switch it on, set them to allow if available - unless the print in your data plan charges you extra, o2 don't but I can't vouch for others, so check first, just in case.
Some newer phones have other tricks, like streaming other devices like PS3s and stuff but honestly if you're at home use the computer or some such.
Basically depending on where you are set your phone up to prefer the fastest connection protocol available, this is simple enough, though if you have pay as you go or stipulations about the likes of 3g then weigh up cost vs. speed, unless it's 3.5g the difference isn't massively appreciable on mobile sites, which have been purposely slimmed down for your liking.
Step 2: Browsers?
There are a variety of mobile browsers out there, my preferred one for any phone supporting java is without a doubt Opera Mini. It's a very fast browser that runs nicely one any old mobile, I have been liking opera lately and the synch function was nice for not having to set my bookmarks again. Also it's nicely animated. One thing that bugs me is that it's good at caching but you don't get tabbed browsing unless you have opera mobile, which costs, if it's already on the phone though, lucky you having tabs makes browsing a lot more like a real computer.
For windows and symbian phones opera mobile's nice butskyfire's free. Though windows mobile also gets firefox, well Minimo - one I haven't used personally but have heard nice things about, plus it's got tabs.
Choosing the browser is all personal, there are others out there, some phone's have dedicated versions of OS's out there that may mean seeking out a specific browser. If you do have a java phone, my advice is just get opera mini, not plugging them here but it's just made things so much better on simpler phones for me, plus the download's miniscule.
Step 3: RSS - Using Feeds
The sweet thing here is that you can save a lot of actual browsing and bandwidth, also by automating them, (something like, options, schedule download, choose schedule) you don't actually have to do anything other than check when you want.
By using RSS feeds for stuff like news or sites you like, such as textsfromlastnight - a favourite of mine you can save mobile browsing effort, especially with sites where you're just reading the updates and not interacting with them.
Step 4: Browing Itself...
The Back button is your friend - By using the back button to go back to the root of a page to go to a different thing you don't download over and over, plus it's quicker because the page will still be cached, though some browsers don't cache whole pages there will be less downloading involved. Plus the less you download the easier it is on your battery life.
Pick and choose your battles - Some sites are just too bloated for mobiles, sticking to mobile sites isn't a must now, a lot of browsers have clever tricks to help and download speeds are good enough to keep up with them but too much content will be slow.
Images - You can choose the quality of images and whether to display them using the browser settings, play around until you find a nice balance, it's phone dependent, on a smaller res screen low quality images will still look sharp but choosing what you prefer's the key here.
Online conversions - Yahoo and some other sites have adapted for mobile options, this is pretty hit and miss but for text based sites it's often OK and saves your phone the work of figuring out how to display the full size ones.
Pan and Zoom - by choosing the right text size for you and using pan and zoom functions you can find the comfiest way of navigating pages smoothly for you, also changing between landscape and portrait can make a big difference.
Downloading vs. Online viewing - When given the option sometimes looking at a big html page on the phone is much harder than viewing a PDF or Ebook, I make use of a little Java based PDF reader to read PDFs at the moment and it's a lot easier than viewing a big page. The other upside is that a dedicated download is often much faster than loading a page the same size, plus you can look at it later on the computer.
Step 5: Roundup
Not everybody likes mobile browsing and some never will but by making good use of mobile internet you can have a lot of those functions that seemed reserved for smartphones and PDAs without shelling out or changing to a format like qwerty keys or touchscreen, which some people just don't like beside a normal mobile.
One key thing I didn't discuss is Data plans and the like, I haven't been on pay as you go in a long time and personally just have an unlimited web bolt on added to my contract, I got it because I had a free option and I did actually like using the mobile web even back three years ago, it's actually been a handy resource for me for some time, though picture messaging's back and forth, good as an illustration of point but mostly it's just a good tool for obscenity through jokes or photos you know you should never send.
Hopefully this helps those that find it and opens them up a bit to things beyond standard browsers and occasionally checking the news when there's nothing better to do. Information age and all that.
Also wow - I wrote this sensible, gotta be an achievement for me.