Note (Jan 2011): this guide is pretty much outdated. I might write an update soon.
What is MAME? It is an emulator intended to document the hardware of arcade games systems. Of course, for most average users it is the side-effect of being able to play more than 3000 unique games that’s the important thing.
Well, that’s all well and good, you say, but how do I start? I’m glad you asked.
First, you will need to download MAME itself. If you run Windows, you can download the official release which is run off the command line, but I would recommend Mame32, which has a really nice GUI. For Mac OS X folks it’ll have to be MAME OS X (not very imaginative, yes) or SDLMAME, which is also the best option for Unix/Linux systems.
Next, you will need the ROM images*.
You can download some freely available ROMs to test. Place the downloaded ROM files into the roms folder where you unzipped MAME to.
To obtain more, Pleasuredome is the best way if you can work BitTorrent. The total size of the ROMs stand at almost 16 gigs currently, and so might take a while. The MAME ROM torrents are ratio-free but please do not abuse the ratio. Some games require CHDs which are compressed hard drive images, but these are generally not worth it as most PCs are too slow to emulate these games properly.
Or if you prefer, you can request for one of the Lazarus guys to burn you a copy. Read the instructions carefully, and note that I have never used their services.
That’s really all you need to start playing. You will probably want to grab the “Extras” torrent from Pleasuredome too. Lots of niceties such as screen captures and photos of the cabinets.
Additional stuff to grab:
* downloading of ROMs is illegal in most cases. You are downloading at your own risk.