Crossbow accuracy

I have been making and shooting my own crossbows for a while now and was wondering how you can improve the accuracy of crossbows although mine shoots reasonable groups. Does the accuracy, apart from the user, come from the bolts or from the crossbow? if your bolts shoot high to the left, how can you shift the grouping over bearing in mind that the crossbow has been made to a standard ie everything made square, not out of line and with open sights. 
Is it string, bow bolts that play an important part to accuracy. If bolts are the factor how did they weigh them back in days of old? Is it bolt placement or how quick you pull the trigger especially using a skane type bow. How accurate were crossbows of the time especially if hunting small game for the medieval Sunday pot

The crossbow is the more or less "fixed" part of the accuracy equation; the shooter is the variable.  

Just like with guns, if your sights are adjustable you can set them so that the arrow goes where you aim; but almost everything else is pretty fixed.  If you don't have adjustable sights, then you must learn to shoot "kentucky windage" style to hit what you want. where you want.

Other than that it's experience.

Effectively a crossbow is a shooting machine, it will always fire in exactly the same way, unless it has a wooden prod which might lose power through an afternoon of hard shooting. If the bolts are all well made and perfectly matched they will all fly in exactly the same way. There are no significant variables I am afraid, apart from the loose nut at the end of the stock......

crossbow accuracy is a lot like gun accuracy with much lower velocities.  If drawn square, the bow itself should shoot the same, shot for shot.  What Does vary is projectiles and the shooter.  Lighter/heavier/longer/shorter/ straighter/stiffer/thicker/balance:  all those things matter in your bolts, and I've been told some of the medieval shoots in Europe are done with the same bolt every shot... and you load the bolt with the same side up.  Everything matters in the projectile.
Second point is the shooter.  In the case you cited (shooting high and left) try banking your bow limbs slightly to the right and lower your aiming point.  Be aware that most shooters will slightly disturb their aim on release, moving a bit right or left.  Fortunately for most folks the boggle goes the same way every time.  If you're accustomed to shooting powerful rifles or shotguns, you may be flinching a bit in anticipation of recoil that never comes.  There are a thousand things to learn about shooting and we can't discuss them all here, just remember that you're looking for Tight Groups.  If all your bolts group closely in one area, it's easier to move that area where you want it.  Bolts that go all over the place are much more difficult to correct.  So close grouping at 10 o'clock is much more hopeful than a shotgun scatter all over the target, the ground, under the grass, etc.  And keep practicing.  Geezer.

More on shooting.  I have encountered shooters who constantly shot low because they were raising their heads (and consequently lowering their bows) on release to see where the bolt struck. Your bolt does not leave the bow instantaneously.  You should wait, motionless until you see/hear the bolt strike the target before moving. (okay, if you're shooting say, 100 yards, you don't have to wait the second and a half till your bolt arrives, but stay still a few heartbeats.) Second biggest problem I encounter is from shooters who don't draw the bow exactly even on both sides.  A mark or bit of colorful thread around string center will help a lot there. Third problem: banking the bow right or left. Lots of right handed shooters tend to bank their limbs left to help line up their eye with the bolt. Banking left shoots left.  Banking right shoots right.  Banking your bow will also help you deal with cross-winds, unless it's really blustery, in which case you are SOL.  
So relax, control your breathing, cultivate stillness and keep shooting.
Geezer.