LM386 - common simple power amp
LM386 amps are very common, most electronic shops sell this chip, and when built correctly will provide a simple power amp for little cost. This amp is a 8-pin DIL package that is capable of 325mW (thats around 0.3W) from 6V and may well provide over a watt from the maximum power supply voltage of 15V. Gain can be varied form 20dB to 200dB, the output is biased automatically to half the supply voltage. For an extremely portable amp, this coupled with a small speaker and a few batteries would do the job well. There are claims that they life this amp will give from one set of batteries is very high, I have never had the batteries run out when I have used it before, and these were very cheap buy 10 for a pound at the boot sale offer batteries. I don't recommend them though, they have rubbish life (probably to do with the fact they weigh half of a Duracell battery) and they leak too (battery acid is dangerous).
I have only ever built one of these amps, and that was a kit so I cannot provide that circuit despite it having good performance. You may notice that the component count for this amp is quite often high - but the components are small. This makes it a little more complicated to build this on strip-board, although it should be easily done.
The one I have built has had many past operations, but recently I have put it in a set of surround sound speakers, coupled with a TDA2822 amp that powers the front channels. With 12V, this little amp provides quite a comfortable volume into the rear speakers (each a 0.25W 50mm ex-PC speakers), quality doesn't matter much for the rear channel because most of the work is done by the main amp and speakers.
As can be seen by the schematic, it shouldn't be too much effort to build this circuit (even for beginners). Just make sure you do get the chip and the electrolytic capacitors the correct way round.
If you are not running this amp from batteries, a PSU should be simple to obtain, just a DC power pack should be enough and they should be easy to pick up, get one that will provide about 12V and around 100mA or more. The higher the voltage and current it can provide, then the more power you can get at the output. From this voltage, you should be able to obtain around 1 watt, that is what I am using (to be honest I am a little worried about blowing up those 0.25W speakers. If I do, never mind, I just buy some Mylar equivalent because they have a rating of 0.5W :-)
That's about all I can say because the applications of this amp is very wide (radios, tape decks, intercoms and even power inverters!).