[recommended pre-read: what is sous-vide?]
All you need is some way of packaging the food without air, and a temperature controlled water-bath. That’s it.
PART 1: Air-extracted packaging
The simplest method is the water displacement method using a ziplock bag. This requires no appliance, and has the advantage of being able to bag liquids. Also, it is gentler on the item being bagged, and useful for delicate food such as salmon. Rather than try to describe the method, it is demonstrated at minute 1:54 in this video from Douglas Baldwin. Other methods include nearly completely sealing the bag and using a straw to keep one corner open, then sinking the bag into water and extracting the straw and closing the final part of the seal. Or, invent your own method.
Entry-level vacuum packaging devices like the FoodSaver are good, and create a tighter seal between the food and bag.
The main downside to the FoodSaver is that it is not possible to bag liquids (they get sucked up into the machine). It can be solved if the liquid can be frozen then bagged and allowed to thaw in the bag. In most situations this is not an issue, but it is something to be aware of.
The ultimate device is a chamber vacuum sealer. I have one of these and I probably use it more than any other single appliance in my kitchen (with the possible exception of the coffee maker). The bag is placed in a chamber and the air is extracted from the chamber (and thus from the bag), the vacuum is held while the bag is sealed inside the chamber (you can see a sealing bar under the lid, it meets another bar (not seen) on the floor of the chamber), then the air is let back in. Liquids can be bagged without difficulty. It can also be used for pressure infusions, degassing liquids, compression and more.
PART 2: Water-baths fall into three categories.
1. Immersion circulator: A heating element is immersed in the bath, and a water pump circulates the water to maintain temperature uniformity. Polyscience (a scientific equipment company) were pioneers in immersion circulators, and they now have entry-level models for the home. There are a range of other options appearing now, for example the Anova is highly regarded, as is the Nomiku.
2. Convection bath: The bath is heated, and convection currents distribute the heat without the use of a pump. The Sous-vide Supreme is the most respected in this class. It has been rebranded by Breville, and is available from electrical retailers. Sometimes known as a water oven.
3. External PID: A rice cooker or equivalent is connected to an external device (PID) that monitors water temperature and cycles power on and off to maintain a target temperature. These are the least expensive if you already have the cooker. There are a number of these devices appearing now, here is an example: http://www.codlo.com
Circulating and convection baths serve slightly different purposes. The Sous-vide Supreme is insulated and good for vegetables (they need higher temperatures), and eggs (they are not buffeted by the circulator). And because it is non-circulating, food (such as stock ingredients) can be placed directly into the device (without bagging). I use the Polyscience circulator for most protein, and for long cooks (e.g. pork belly: 60C for 2 days). It can also be used with pots of varying sizes, depending on the food to be cooked.
This can be done under a grill or in a hot pan. Searing beef before cooking sous-vide will kick-start some flavour development. Post-cooked searing will create a tasty crust. Both pre- and post-cooked searing can be combined. The aim is very high heat so as to just brown the surface layer of the meat. A blow torch is a good solution because it heats to high temperatures. Select a trade-quality torch (rather than kitchen varieties) that use MAP-propane as fuel. This fuel source will not leave an aftertaste.