Finally figured it out after a couple of hours and some stupid brain-dead attempts. Even better, it is actually pretty easy to set up and isn't quite a waste of time as some suggest. It is easier to buy Bitcoins than it is to mine and perhaps the power cost is not favourable but I figure that I need to have my computer on for many tasks anyway so why not do some mining in the background. A lot of things I do are low intensity jobs like email, word-pressing, social networks and writing articles. Running a Bitcoin miner really needs to be done by a graphics card, GPGPU card or a custom rig (FPGAs or whatever). This article is partly for my own reference although it may prove useful for others.
Introduction -- getting a wallet
If you have read my previous article about what Bitcoin is, or you know what it is, then you may have already started to read the Bitcoin wiki or the the Bitcoin forums. The former is a good place to build up your general knowledge of what the currency is and how it works, while the latter provides a good perspective of how the idea has evolved. You can read the discussions on the forum about various events and the community's reaction to them. You can also use them to gauge the type of people that the currency has attracted so far.
To get started on the collecting process you will be told to download a wallet. For ease of explanation: the wallet is a program which holds your Bitcoin addresses. You can essentially have as many addresses as you want (there are some caveats, look up wallet back ups) and these are the 'places' where you hold the Bitcoins. One part of your address is public (which deals with deposits) while the other part is private (which deals with withdrawals / expenditures). The public address is something that you can freely share as you wish, coins can only be deposited and not taken from it. Then vice-versa for the private key. If you share your address then you can receive donations but some people don't share their address in a public domain as they don't want it linked to their name. The first step is downloading a wallet, I'd suggest trying the Bitcoin-qt program (the main one). This gives you a good impression of how things work, you will become familiar with the idea of the "confirmations"/ addresses / transactions and synching to the network. The latter will take 8+ hours when you run the program for the very first time; you need to synch with the network, there are hundreds of thousand of ''blocks'' (includes information about mining and transactions) that your computer will confirm. The block checks start very quickly but then get painly slow by the end, I think my computer spent in excess of 12 hours (4 year old machine) but I left it on over-night so wasn't so bad.
Bitcoin mining
At first I was scared to mine bitcoins as the general forum consensus is don't do it, so I figured I'd give Litecoin mining a shot. Litecoin is supposed to run better on CPUs and is an alternative to Bitcoin which is solved better on GPUs. I think Litecoin is a good alternative and the supposed redundancy here is not a bad thing (cf: Taleb's thoughts on redundancy and fragility). For Litecoin I downloaded the appropriate programs and got myself the equivalent Litecoin-qt wallet but I couldn't figure out how to get mining to work. There is a miner built into the Litecoin wallet but there is very little way to check if it is working except to wait and see if you get lucky, unfortunately I'm not patient enough for that and solo mining probably isn't the smarter. I checked out a couple of tutorials and downloaded a few more mining programs but no luck.
After much frustration and overlooking the obvious (which I'll return to) I decided to go back to Bitcoin and see if I could get mining to work there. The tutorials and programs for Bitcoin are similar but the mining pools and their websites are far more mature. This latter point is how I finally figure out my stupidity. When you open the mining program you need to input the server url address, your username, password and the port number. What I didn't appreciate is that the username you use to sign up to a mining pool website is not the your actual mining-pool username; if your username for their website is John then your mining username might be John.1 (or similar). That vital piece of information had be stumped for hours. None of the tutorials I found mentioned it and the Litecoin websites don't mention it (they probably assume good familiarity with bitcoin); however, the Bitcoin mining websites such as bitcoin.cz make it much more obvious what your mining user name is plus they give you a different password that you use to access the mining pool. Again, it wasn't so obvious but in hindsight I can completely understand why they do it (security).
Suggested Bitcoin miner: Guiminer it runs on modern graphics cards (circa last 4 years) such as NVidia CUDA enabled cards 8xxx and newer, as well as ATI cards 5xxx and up (if I have the details correct). The mining programs display your hashrate which let's you know that work is being done. If you don't see a hash-rate ("computation speed") then you may not be connected to a server, as fate would have it the first Litecoin server I tried to join seems to be down. The bitcoin.cz website is mature (imo) and it shows you how many blocks you have mined (or rather how many shares you have of the blocks), it shows your mining pool usernames and passwords in an obvious format (fool proof!) and it shows you what your earnings are for each block you helped to mine.
Litecoin Mining
This is an alternative to Bitcoin as stated and is, at time of writing, 12 months old. It copies all the key features of bitcoin but has a slightly modified implemention. For example it will have 4 times as many coins in circulation as Bitcoin (84 million instead of 21m) and the mining process (block discovery) is supposed to favour CPUs as the calculations are more memory intensive. The idea is not to compete with Bitcoin but the complement it. It is less rare and it will provide miners something else to do once all the Bitcoins have been mined (afaik).
The programs used are fairly similar to bitcoin so once you have your Litecoin wallet then you will need to download the appropriate miner, the favoured version is ScryptMiner (there is a GUI version too). The overall process is pretty much the same too: find a mining pool website, join up, get your *actual* mining username and password then configure your miner to point that the mining pool's url.
Getting paid
As part of a pool you get a share in the rewards for all the blocks that are found/solved. If you are running a basic desktop computer then don't expect a huge reward but every little bit can help and mining on your computer is still faster than trying to claim free coins from the various sites that give coins away. Once you have mined enough shares of the coin blocks then you are entitled to get your share of the coins. There is a threshold that you have to achieve in order to get a payout, naturally taking out small amounts is an unnecessary expense. Once you have built up enough coins then you can put in your address and take the winnings manually but generally all the mining websites have an automatic payout function. It is worth setting that up and forgetting about it. Just mine and take the rewards as they come.