Practicing has mainly two purposes: you can practice to learn new music and work on pieces you already know or do excises that will help you improve specific aspects of your playing.
Working on solo pieces and etudes will of course improve your playing but it is good to have a daily routine that you can include in your warm up and specific exercises to focus on one thing in particular like lip trill exercises, long tone, flexibility exercises etc.
If you are a beginner, you will mostly follow your band method or any other method book that your teacher gave you. Some students will only pick up their instrument during band practice. I recommend that you play about 30 minutes/day, five times per week on top of band rehearsals.
Once you've played for a year or two, you can warm up by playing scales and arpeggios to develop your technique and practice a combination of solo pieces and etudes. You can increase the duration of your practice session to 40-45 minutes. At this point, you need to expand your range and develop reflexes. That is why scales are very important here. Learn them in every key even if it's not the most exciting thing to practice. If you've practiced, let's say, A flat major a thousand times, you won't panic when you see four flats at the key signature!
For intermediate level, it's pretty much the same as before except that the aim of your practice is more to polish what you have already than going further so you need to include long tones, lip trills and flexibility exercises in your warm up on top of scales and arpeggios. It is very tempting at this point to work only on fast pieces and fast passages but don't neglect slow music. Practicing slow movements will do great things for your sound, phrasing, intonation and musicality. The pieces you will play at this level will require more endurance and high register skills. Take time to do chops building drills like the Caruso technique or any other routine 3-4 times/week.
Once they've reached a certain level, some students are satisfied with just playing in the band and don't practice much individually. That's okay with me as long as they don't become a drag for their colleagues. I sometimes ask them to practice a bit in the weeks before a concert if they're struggling. It's usually no problem. I understand that they can have other interests or have quite a lot to do in school especially those preparing for college.
Advanced students who want to become professional musicians should be playing a minimum of 2-3 hours/day individually. At this point, there's no magic trick. Practice a lot, practice well and you'll get where you want. Have a complete routine that covers all aspect of your playing and do it every day before playing your pieces, etudes and excerpts. Don't do the same things all the time. Be creative and add new elements from time to time. You only see your teacher once a week so you need to be the teacher the rest of the time. Don't be satisfied with just "being able to play it". Everyone who has a minimum of talent and practices for long enough will be able to play most of the repertoire at some point. You need to make the music interesting so people will remember you for the right reasons. Practice the musicality. Come up with your own ideas and make them happen. This starts in your practice room. It won't just magically happen in concert!
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.