Heat the adhesive under the old guard with a hair dryer. Be careful not to overheat or you can damage the underlying surface, causing blistering.
Peel the old guard off as the adhesive softens. Hold the dryer in one hand and peel with the other as you go.
Remove the remaining glue with naphtha and cloth. Naphtha is a liquid solvent that will remove the glue from the guitar without harming most finishes.
Choose a new guard that matches any "tan line" left on the guitar. Tan lines are discolorations on the original surface caused by the original guard. If the tan lines are severe, you may need to replace the guard with one of identical size.
Float the new pickguard on a bed of water and use a squeegee to force out bubbles. This means you'll apply a small amount of water on the body of the guitar -- not enough to get the entire guitar wet, but enough to make the pickguard appear to "float" on the surface. Once you squeegee out the bubbles, the pickguard will be stuck to the body of the guitar.