What techniques would you suggest for cooling a lager during the lagering phase? Further, how important is the stability of that temperature?
Find a 4.2 cubic feet (or larger) minifridge on craigslist. I usually see them go for around $50 to $70, but YMMV depending on where you live. With the shelves removed, 4.2 cu. ft. should be large enough to hold a carboy.
Grab a temperature controller and use it with the minifridge. This will allow you to regulate the exact temperature inside, making it perfect for lagering, and for fermenting any other style of beer at the exact temperature you want. The Johnson Controls models are often highly recommended, but if the ~$80 price range is above your budget, I've seen them go on eBay for much less. You can also check your LHBS or look online -- there are often people getting rid of kegging setups that include them.
Cheapest = Brew in the winter =P
I know this is an old question, but I see that it still gets some hits from time to time so I thought I would add a bit to my answer.
One of the benefits of this approach (besides the fact that no extra equipment is required) is that it gets you back to brewing's roots.
Seasons used to influence brewing in fundamental ways. The obvious way is that you are going to have warmer fermentation in warm weather and cooler in cold. But also because our taste in beer tends to go towards lighter in warm weather and heavier in cold.
Lagering was only available if you had cold weather or if you happened to have a handy cave system available. Technology definitely allows us to produce a more consistent product if we are willing to shell out the money.
However, I think there's something to be said about sticking close to our brewing roots. I personally find it fun and feel like it forces me to brew a larger variety of beer rather than sticking to the same few styles.
Dig a hole in your back yard! Seriously a small bunker type hole just big enough to fit your brew is fairly cheap to build. Build a well insulated roof for it, make sure it's sealed to keep out pests. Underground temperatures are much cooler than above ground in warm areas, and much warmer than above ground in cooler areas. The temperature stays fairly consistent. I recommend digging about 6 feet in your back yard and drop a thermometer in there and throw some insulation on top and see what the temp is.
Another option is underwater brewing in a pool (if you have one) but this is much more complicated and kids complain when they can't swim cause dad is brewing again. lol Here's a video of an undersea brewery!
This seems to be cheap and easy solution. If you have a cooler, you can probably pull the whole thing off for $20.
Here are a couple of YouTube videos on how to use the Cool Brewing Fermentation cooler.
There's also the Cool Brewing fermentation cooler ($55). It works surprising well as long as you change the ice packs (or whatever you use to cool it) every 12-24 hours.
In cold temp/climate. Use a temp controller. Basic unit is about $20 + parts to make an electrical box and cord for it. Put the sanitized probe into your fermenter. Wrap the fermenter with a blanket. Place it on top of a heating pad that is plugged into the temp controller. Set the desired temp and stash in a safe home in the unheated garage or shed. Great lager in 6 weeks or so.
In warmer temp/climate. Same as above except build a small box out of styrofoam insulation. Connect the controller to a small window AC unit that blows into the box. You'' need more space and a way for the AC condensate to drain.