How quickly you determine how the oil pattern is affecting your ball and how quickly you adjust to it can greatly influence what your score will be.
Most accomplished bowlers will use their practice shots before league starts to see if they can find clues to what the pattern is. Sometimes you may have the advantage of being told what the pattern actually is and even have a graphic representation of it available.
You should, over time, establish a shot and starting point that you are very comfortable with, This would be the shot to start with on any given lane, paying particular attention to where it hits in relation to your intended target, and how it got there. If the ball finished right of your target, you should move your feet right, only a board or two at a time, on the approach and try to use the same target, again observe how the ball reacts and adjust again if needed. Conversely if the ball finishes left of your target you would start moving to the left, again only a board or two at a time, and still using the same target.
When you encounter very dry lane conditions, which would cause your ball to move very aggressively away from your intended target, this may require that you move and also change your target line. You could also be on a lane condition that is heavily oiled, in this case the ball will skid through the oil and then grab the lane when it gets to the un-oiled part, this kind of pattern may even require a ball change.
Lane conditions change constantly even while you are bowling, this is caused by the oil drying up or carrying further down the lane, making your ball either over react or not react as well on the back parts of the lane. Because of this shifting of the oil pattern you may have to make adjustments throughout your bowling session.
Oil and conditioner patterns greatly influence scoring conditions, being watchful and aware of the need to change your delivery will help shift that influence in your favor.