Practice 1 line at a time first. Since 3 stave notation is new to beginner organists, it is not surprising why they find it so difficult to read all the lines together at first. However, we should remember that even two lines of piano scores were difficult to read at first. Therefore, I suggest you practice one line at a time in the beginning. For example, when you take a new organ composition, don’t attempt to play the entire organ score with pedals, but practice the right hand part at first, then play the left hand part, and, finally, master the pedal part. This will be the hardest task.
Practice 2 lines later. When you can play your solo parts at least three times in a row correctly without hesitations and interruptions, put 2 lines together and practice them. You can work in the following dispositions: the right hand and the left hand, the right hand and pedal part, and the left hand and the pedal part. As in the previous step, try to achieve some fluency and play each disposition without mistakes, with the right articulation at least 3 times in a row correctly. The most difficult disposition undoubtedly will be the left hand and pedal part. Here you will have to repeat the most times. Stop at each measure when you make a mistake, go back a few measures and correct each mistake.
Finally, practice 3 lines. If you are honest and practice sincerely the two previous steps this final step will not be as hard as it have seemed to you originally. Now you are ready to play all parts together. Again, work in smaller fragments for best results and correct your mistakes.
Note that every step requires practicing in a slow and comfortable tempo. Although the concert tempo might be much faster, don’t worry about it at first. You will be able to play up to tempo naturally when you are ready.
Practice sight-reading the same way. If you are interested in reading music at the organ, you can try practicing 371 Harmonized Chorales by Bach. Although their are short but their harmonies are spectacular. We know that Bach never wrote a treatise on harmony. But these harmonisations are like a real textbook of harmony. Many theorists after Bach analyzed them and developed a system of tonal harmony.
You can practice these chorales (with bass part on the pedals) to improve your sight-reading abilities at the organ. Apply the same above steps and play solo voices, combinations of 2 voices, combinations of 3 voices, and finally, the entire four part texture.
If you really want to develop unbeatable sight-reading skills, check out my systematic Organ Sight-Reading Master Course. To complete the practice material of this course will only take 15 minutes a day of practice but you will learn to sight-read any piece of organ music effortlessly.