Flying is basically a procedural thing and so practice makes perfect and relaxation and concentration on following procedure will help enormously.
As others have said the critical part is the approach not the landing. So when flying a conventional circuit you should arrive in the final approach at about the right altitude and you should pick an aiming point near the start of the runway, but beyond the threshold, often that's the numbers, and position it about 1/3 the way up the windscreen and then keep it there. As you pass over the threshold you should round out into straight and level flight and move your gaze to the end of the runway, then close the throttle and pull slowly and steadily back on the yoke or stick and if you've done it right the aircraft will settle gently but firmly on the main wheels as the stall Warner starts chirping merrily and the yoke or stick meets your tummy!
That will work for most training aircraft and many more sprightly light aircraft, in my experience.