Boresighting is great and will save you a lot of time. If you don't want to buy a boresighter, most gunshops/gunsmiths can do it fore you. The last time I tried to scope a rifle (ar15 with a 4x scope) without boresighting it took me close to 30 rounds.
If you still don't want to boresight, here are some tips that I learned (the hard way
).
1. If possible set the rifle in a rest or vise that will keep it from moving. Look down the sights or bore and mark where they line up at about 20 yards. Carefully mount the scope and adjust the crosshairs to the mark (do not let the rifle move). This should get you on paper at 20 yards.
2. Get the largest target possible (I'm talking 3'x3' or bigger) and shoot from a rest. Shoot 3 rounds to begin with (and hope they hit paper), they should group close together. If the rounds don't group then you have another problem that you need to fix first (probably a loose scope mount). After the initial group, begin adjusting the scope towards the center of the target. If you are comfortable with your shooting ability you really only need one shot per adjustment.
3. Work from close to far: get all your shots to hit dead center at 20yrds then move to 50yrds, then to 100yrds. Because of the ballistic trajectory of the bullet, dead center at 20yrds will not be dead center at 50, but it will be close enough to be on the paper. Dead center at 50 will get you on the paper at 100yrds, and from 100yrds you should be able to zero the scope at any range you want.
Zeroing a scope without boresighing is quite possible, it just takes a lot of time and ammo. Boresighting lets you skip to step 3 and will require much less adjustment to initially get on center. I did the above process with my AR and my FAL, but I would never consider it with something like a .300win mag.
Edit: The one shot zero that .38 special described is great and the fastest way to get on target if you have a good solid rest. My rest isn't very good and I couldn't be sure of the rifle not moving, so I used a target with 1" lines running in a grid. I would fire, see how many inches off the bullet hole is, move the crosshairs 3 clicks then fire again. The distance that the point of impact will move per click changes based on the range to the target. Your scope should say how much it moves per click, usually 1 MOA (approx. 1" at 100yrds) but some scopes differ.