When mounting a scope on a gun, it's recommended you boresight it (align the crosshairs with the barrel) before attempting to sight it in. This saves both time and ammo! Here's a method which works on most bolt-action rifles & handguns.
Difficulty: Easy
Time Required: 15 Minutes
Here's How:

   1. Check if the gun is loaded; if so, unload it.
   2. Mount the scope on the gun if it's not already mounted. Make sure the scope and mounts do not interfere with the operation of the gun (by conflicting with the throw of the bolt handle, for example).
   3. Remove the bolt from the gun. This is usually very easy and only requires holding the trigger back or engaging another type of release while pulling back on the bolt (after opening the bolt, of course).
   4. Place the gun on a solid rest of some type that won't mar its finish. On cushions on the hood of your truck, across the back of a sofa, or in a solid shooting rest are all choices that will work.
   5. While looking through the bore (barrel), carefully align the barrel with an easily identifiable distant object. It can be as close as 40 feet, or as far away as you like.
   6. Without moving the gun, take a look through the scope and note how far, and in which direction(s), the crosshairs are from the object in the previous step.
   7. Using the crosshair adjustment screws on the scope, adjust it (see Tip 2 below).
   8. Eyeball through the bore again. If the gun has moved, re-align the bore with the object.
   9. Check the scope again and re-adjust as needed.
  10. Repeat steps 8 and 9 until the bore and scope point at the same spot.
  11. After boresighting, head to the shooting range to sight it in and start shooting at close range (I recommend starting at 25 yards, no farther than 50 yards).
  12. Congratulate yourself on a job well done and a savings of ammunition and range time!

Tips:

   1. ALWAYS keep guns pointed in a safe direction.
   2. When adjusting a scope in this manner, you must go the opposite direction stated on the scope. Example: The bore is aligned with a target, but the crosshairs are right of it. You must turn the windage adjustment screw "right" to correct this.
   3. Similar results can be had for guns other than bolt-actions through the use of a boresighting tool. These are often costly, but most gun shops own one and will boresight your gun for a small fee.