Your post isn't clear whether you want future access to the hole. If you do, and the hole is small enough, you can use Jeff's trick.
If you want it to simply go away, do the following.
1. Find a construction site nearby and get a small scrap of plasterboard and two small sticks.
2. Go to the home improvement store and buy the following. Spackling compound. Spray texture. A box of flathead screws. An abrasive sponge or dedicated open file. Paint and paintbrush.
3. place the two strips of wood behind the existing wall and secure them to the wallboard using the flathead screws.
4. Cut the scrap plasterboard to fit in the hole, leaving a small gap on each side.
5. Screw the new plasterboard to the strips in 4 places, two on each strip.
6. Fill in the gaps with the spackling compound and let dry
7. add a second coat to fill in the shrinkage and to cover the entire new section and an inch or two of the existing wallboard. Let dry.
8. Sand this down until level and smooth
9. spray with the texturing compound. Let dry.
10. Paint to match existing wall.
You will never be able to see where you cut into it.