If you have a laser bore sighter, use it to get on the paper.
I don't, so....
I attach my scope and head to the range. Here's what I do: Be sure to use a gun vise to hold your rifle. Its WORTH the extra few bucks for one. This is necessary for this technique to work. It will minimize the movement which will allow you to get on the money immediately. It will save you ammo $ in the long run too.
Vise clamp your gun down and pull the bolt out. (I'm assuming you have a bolt action.) sit back and look through the bore to your target at fifty yards. Line up the bore and then look through the scope and get them close on the bullseye.
When you feel your relatively close to the target, pop the bolt back in and take a shot at the bullseye at the 50 yard target. Load another round and do the same thing EXCEPT after you line up the crosshairs on the bullseye, crank your scope cross hairs to your last shot taken. Be sure to not move your gun after eyeing the bullseye and then moving to the new location.
Bingo! you should be on target or very close. Several shots may help, but isnt always necessary. Move your target out to 100 and pop one off. I'm usually looking to be about 2" high at 100 to be on target at about 200-215 yards. Move your target out to 150 and then 200 and get comfortable with it.
I've dead zeroed guns with two shots!!
Hope this helps....Frank
You can't swap the scope from one rifle to another in a different caliber.