Ear training is the key to improving intonation. Audiation, or internalizing pitch is the key to putting your finger in the right place. Think about a dartboard- the bullseye is the correct pitch. If you are not on the bullseye, how close are you? If you are playing an instrument without having a good intonation target it is like playing darts with your eyes closed. Someone will get hurt!!
Professional players make intonation mistakes, but very minute ones. Students miss by a mile. What is the key? Ear training. You must sing!
My other necessary intonation work is developing the right concept of intonation. Students don't listen for intonation the same way that people that have good intonation. Most times, if you ask a student to play a scale and they miss a note, they progressively get worse as they go up and down the scale. If they play an open string they may correct, but the whole of the scale is wrong.
People with good intonation listen to the intervallic relationship between tonic (the first degree of the scale) and the note they are playing. It doesn't matter if you miss one note, because the next can be in tune based on the relationship of that note to tonic. To practice this, I always have students use a drone when they play scales. It immediately snaps their pitch into place. I can hear that drone in my head and when I practice sometimes I will drone a pitch and sing the scale, or drone the pitch with my voice and play the scale.
Give it a try and let me know how it works for you.
Best,
Brian