Rests are sometimes tricky because they require you to play nothing to do something. They look like an empty space on the page but they are really not empty in the music; they have a count, they have a position within the measure, and they have a role within the phrase. It is easy when a student thinks of a rest as a non-entity that the next note comes in late or early or hurriedly.
The first thing to do is to add a sound during rest rehearsal. It is not necessarily a sound you would make musically, just a sound you will make counting. If there is a quarter rest on the second beat, say the number two while you hold your silence on the instrument and your voice. If you have a half rest occupying beats three and four, count both beats fully, without making them shorter. The feeling of silence as part of the rhythm will become part of your body. The beat will continue while you are playing nothing.
Try the rest on a single measure before trying an entire line. While you are clapping the notes, keep your hands off while there is a rest, but keep counting out loud for all of the measure. It should be four beats in a four-four measure; your voice should keep going for all four beats. The hand has rest in it, but not the beat. Play the same measure while singing or playing and keeping the count on your side, but still in your mind.
Rests become even more confusing sometimes when the eye wants to get ahead. You see a rest and then you go on to the next note and forget that a rest exists and that it has some value. A pencil might be able to assist you here. Lightly circle a rest that gives you trouble or write a small number of beats above it. Do not add every rest that is on the page, just those that are causing you to miss an entrance or a beat or to pause at all.
A metronome may be a very helpful tool in rest rehearsal, but only if you are slow enough to have time to feel. Set it to a speed where you will be able to count without feeling like you are rushing for the next count. The click of the metronome will continue while you are silent during the rest. Try to notice when your body will be willing to play before the next click. If you feel you need to play before that click, slow down the speed or speak the count more vocally. You are not there to submit to a machine; rather, you are there to feel the gap before the next note.
Rests may be more difficult in places that are right near a bar line, after a difficult interval, or within a phrase that has been moving quite fast. In these places, separate the rhythm from the melody. Count the rhythm for the measure alone. Read the note titles that are just before and after the rest. Put them together to create the complete thing. This will keep the rest from becoming the point at which reading, time, and playing are all combined at once.
A rest is successful when the following note comes out calm and without being grabbed or guessed. The rest has been counted. The beat has gone on. The phrase has had some space within it. Next time you rehearse, notice how the next note following a rest you are used to losing happens in your body. Take the whole rest and try to find that next note a bit easier to play.