The simplest way to power most effect pedals is the good old 9v battery – however this is not particularly convenient or cost effective and in some cases, especially with mini-pedals, not even possible.
As you accumulate and use a few pedals you will probably consider the purchase of, or making your own, pedal board. Once the pedals are attached to the board you will not be able to easily change batteries (Boss pedals being an honourable exception to this rule).
The solution to all your troubles is a mains power supply.
In its simplest form, the classic wall wart style of power supply is easy to use and, with a daisy chain cable, capable of powering a decent number of standard pedals. The Boss PSA-240 is a great example of this type of power supply. It provides 9v DC at up to 200mA. You need to be certain that all your pedals are powered via a 5.5mm plug with a centre negative connection – this is a standard that was set by Roland (Boss) many years ago and has been adopted by most manufacturers as the norm.
The next step is a “brick” type power supply which has connectors (usually again the standard connector) on the box and connects with an individual cable to each pedal (or a daisy chain might be included so that you can expand the number of pedals that can be powered). It may well have a much higher power capability than the wall wart.
This introduces the issue of power consumption – there will be a stated current limit for each output and this should not be exceeded. Usually the power consumption of an individual pedal can be found out from the spec sheet or the web. These can vary widely with analogue boosts, overdrives and other pedals using less than 20mA, some digital pedals requiring as much as 250mA or more and occasionally some of the 9v powered multi effects might need as much as 500mA. You may need to have more than one power supply in order to power your whole board, and in some cases individual power supplies for certain pedals.
Another consideration might be that some pedals (often, but not only older style fuzz pedals) like to have a power supply that is isolated from other pedals – if they don't get this the usual symptom is some pretty hefty hum. In this case it is a good idea to get a power supply with isolated outputs – the T Rex Fuel Tank Junior is an excellent example of this – you can put the troublesome pedals on individual power outputs and the have a daisy chain for the better behaved (but watch out for those high consumption pedals again).
Some pedals have a different power requirement – you might find a pedal that needs 12v or 18v or some pedals that work on 9v will work even better on 18v! A great example of this is the Fulltone OCD pedal which really comes to life with an 18v supply. You might even find a pedal that requires an AC power supply. If this is the case, you will need to look for a power supply that provides a more eclectic mix of options – the T Rex Fuel Tank or Fuel Tank Chameleon may well be what you need – in these cases they include a voltage doubler cable to achieve 18v, but this does consume multiple outputs! Another candidate would be the MXR Iso Brick which has a plethora of output options and may well have everything you need.
So it all comes down to understanding your need – voltage, polarity, style of connector, AC or DC, current consumption and number of outputs needed – once you have a good handle on that, the best candidate might very well be obvious!
Good luck and I look forward to hearing from any one who has any questions or, better yet, come into the store with your requirements and let us help you work out the right gear for you.