There is a large gap between reading Arabic and understanding it, and most students sit in that gap for years without realising how narrow it actually is for the specific purpose of prayer.
The vocabulary of daily worship is small and highly repetitive. The opening chapter, the short chapters most people recite, and the fixed phrases of the prayer itself draw on a few hundred words, and those words recur constantly. Learning them is a matter of weeks of steady attention, not years — which is a very different proposition from learning to read Arabic newspapers.
What changes when you do is hard to describe to someone who has not experienced it. Recitation stops being a sequence of sounds you are responsible for producing correctly and becomes something you are saying. Students consistently report that concentration in prayer improves before their Arabic does, simply because the mind has something to hold onto.
The practical route is to start with what you already recite. Take the chapter you say most often and learn it word by word, then phrase by phrase, then as a whole. Because you have already memorised the sound, the meaning attaches to something solid instead of floating free.
Grammar can wait, and should. A student who learns enough grammar to see why a word carries the ending it does gets a great deal from it, but that is a second stage. Meaning first, structure afterwards.
If you want to go further than worship vocabulary, that is a genuine course of study with a real syllabus behind it, and it is worth treating as such rather than as an extension of recitation class.