Here is how it works:
You can buy ASICMiner shares on btct.co and bitfunder.com (I use Bitfunder).
There are two stocks G.ASICMINER-PT and TAT.ASICMINER. A TAT.ASICMINER is 1/100 of a G.ASICMINER-PT share so it's for people who want to buy smaller quantities.
There are 400,000 total shares in existence but most of them are not on the exchanges. They are the "real" shares that are held by the founders and by people who bought in at the IPO (I think). The ones on bitfunder and btct.co are passthrough shares which mean they get paid a dividend and don't get voting rights.
The dividend is paid every week based on the profits of the company. See this google doc:
https://docs.google.com/spreadsheet/lv?key=0AkPdXsQFT-vIdHRVUjQ5Ql9BQWR6OENLMkhyUktUblE#gid=0You can see in the last column is the estimated dividend for the past seven days. And then on every Wednesday there is an additional number. That is the actual dividend that is paid out per share. It's been much higher than the estimate for the past few weeks because the estimate only includes the profits from mining. There are also profits that come from sales of ASICMiner hardware.
In my opinon, it is still a very good investment. Current share price is 2.44 and this weeks dividend was 0.02653753. That's an amazing 56.5% yearly return (in less than two years you'll make your investment back from dividends alone). Most blue chip stocks pay something like 5% a year in dividends.
You get the dividend every week, typically Thursday morning although the amount is announced on Wednesday.
ASICMiner seems to be the only ASIC company that is doing it right, while both Avalon and Butterfly Labs have been faltering and experiencing significant delays. ASICMiner has consistently held about 25% of the worlds total mining power and I believe they can continue this for a long time into the future (at least for the next year). As they produce more hardware they have (wisely) opted to sell it instead of raises their mining share and risk destabilizing bitcoin. They had originally planned to go to 200 TH/s (more than twice the worlds total hash rate presently) by the end of the summer but they've held off due the fact they have no competition (which was not expected). They spend 50% of their profits investing in more mining hardware.
I admit I am biased as I own ASICMiner shares but I would recommend them as an investment if you have bitcoins you aren't otherwise spending presently.