In most cases, converting a servo to full rotation is a combination of mechanical and/or electrical steps, depending on the servo’s physical construction.
For most servos:
You open the case, exposing the geartrain. The output shaft is a molded part of the final output gear. That gear usually has a physical stop molded into it, which needs to be cut off to allow it to physically rotate through a full circle, rather than being restricted to a set arc.
This output gear is also mechanically coupled to the shaft of a potentiometer, which is used to provide positional feedback to the electronics of the servo. For many modern servos, disconnecting the feedback is a simple matter of removing a small plastic coupler so that the pot’s shaft no longer rotates in sync with the output shaft of the geartrain. Other older or oddball servos may use different schemes of coupling the output shaft to the pot, so this step may take a bit of improvisation. I personally have seen servos that used an offset peg that served as both enpoint stop and feedback coupling (mid-1980s JR servos), and ones that used the potentiometer’s shaft as a press-fit axle for the output gear (Cirrus servos, I think). That latter design posed a bit of a problem, since the pot itself restricted the output’s rotation.
I prefer to take this a step further, replacing the feedback pot entirely, and replacing it with a multi-turn trimmer on the outside of the servo’s case. This adds a little bit of bulk to the servo, but I prefer to use a set center point in the program code, and adjust the pot to zero out the servo at power-on, rather than tweaking it in the software.
Some people go to the other extreme. Since the feedback pot is buried deep inside the servo’s case, and depending on your servo’s design, there may still be ways for the shaft to rotate under influence from the geartrain, a lot of people pull the connections to the pot entirely, and replace them with a resistor bridge that’s essentially the same as permanently fixing the shaft to the center of its range.
Another thing to watch for is whether your servo can be modified for full rotation or not. I think most modern servos can be so modified, but I’ve been burned on a few cheaper models before. It’s not nice to buy a handful of servos, only to open them up and find that the output gear only has teeth over part of its circumference (Cirrus).
There are lots of informational sites on the web about converting servos to full-rotation, including one right here on this very lynxmotion website. If you can find one that uses your particular make and model of servo as the example, that’s great - it’ll probably have all sorts of pictures and/or diagrams to refer to. Otherwise, you’ll have to do a bit of improvisation. It’s almost always a fairly straightforward operation though, and it’s easy to figure out if you look at it with an eye to “how it works”, rather than just “what do I do next”.
As others have pointed out though, while converting a servo may get you full rotation out of it, you lose all ability to hold a commanded position. It will spin in the direction you tell it, at the speed you ask, and then when you stop telling it to go there, or you command it to its center position, it just stops. You don’t get the positional locking that you do with an unmodified servo. An analog servo goes just as limp as if you’d removed power from it, since, as far as it knows, it already is at its center position, and doesn’t need to resist any changes to the position of its output shaft.
I haven’t played with digital servos at all, but from what I’ve read, they will tend to maintain their last commanded position even after they stop receiving a pulse train. This would have the interesting effect of continuing to rotate at the last commanded speed and direction until they’re told to center up. This would certainly make it easy to use them as drive motors for lightweight wheeled platforms, requiring only a few pulses to “set and forget” your motor speeds, but at the added cost of using digital servos over analog. Depending on your setup, it may just be cheaper to use modified analog servos and one of the one-chip servo-driver solutions out there.