The first rule is, the blade should be sharp. SHARP.
But then there are some things about plane assembly that you pick up with experience and aren't clearly addressed in the usual instructional resources.
One of these relates to runout in the blade adjusting mechanism and play in the blade holding mechanism. Basically, when you re-place the blade on the frog/in the plane, set the blade "pin" in the right groove for the right blade penetration through the mouth. Then place the lever cap on, and tighten it using the cam-lever. That lever should be turned all the way, but you can adjust the force applied using a flathead screwdriver. It should be tight, but you should be able to wiggle around the lever cap using moderate hand pressure.
--> the key here is that if it's too loose, the blade will never sit properly. But if it's too tight your adjustment attempts (laterally) wont do anything.
As part of this lever cap placement, pull the blade back as far as it will go, then flick the cam lever.
now, turn the plane over, and adjust the lateral position of the blade so that the blade edge is square to the mouth.
Finally, back out the blade, then slowly bring it back in while making test passes on some wood.
One final note: some woods are prone to tearout no matter what (those with interlocking grain), and a block plane with its low angle of attack only exacerbates the situation.