Every serious trumpet or trombone player owns an Arban's book, and many even practice out of it on a regular basis. Below is a simple routine, using just the first two sections of the book, that you can do in about 25 minutes to keep in touch with the most fundamental priorities of playing.
I owe a great debt for this routine to my good friend and valued colleague Joe Foley, with whom I'm privileged to play in the Rhode Island Philharmonic and elsewhere. Joe is quite possibly the most consistently accurate trumpet player I've ever known, with a complete command of the physical demands of making music on the trumpet. He's a great teacher, and he uses his version of this routine in his own playing and with his students, particularly at times when balance needs to built - for example when an embouchure adjustment has been made or a new instrument or mouthpiece has been purchased - or restored, such as after a period of unusual playing demands. But even when your playing is going along well, this is a very productive way to spend 25 minutes.
Joe's basic concept is the simple starting point: use the digit at the end of today's date, and play every etude in the first two sections of Arban's (about the first 40 pages, depending on the edition) that ends in that same digit. I write this on September 1st, so I would play numbers 1, 11, 21, etc., and then start over in the second section and play the same numbers. Tomorrow I would play 2, 12, 22, etc. This same calendar scheduling can be applied to any set of etudes or exercises; I often do the same with Brad Edwards' Lip Slurs, Kopprasch, even Bordogni/Rochut. I imagine the same principle will apply well to Brad's new book. The beauty of this is that it takes a certain element of choice out of your hands, so that you don't skip things that you don't do well...yet.
As with any practice material, HOW you play is even more important than WHAT you play, and I have some very specific suggestions on HOW to play the short, seemingly simple etudes in the first two sections of Arban's.
As an aside, for this basic routine I read in tenor clef and transpose down an octave. I believe that this is the true middle register of the bass trombone, where we spend most of our time in most ensembles. I often play Bordogni/Rochut this way as well.
I own both the Carl Fischer edition of Arban's edited by Simone Mantia and the Encore Music Alessi/Bowman version. I highly recommend the Alessi/Bowman version, because their commentary is tremendously valuable. If you simply follow their guidelines diligently and carefully you absolutely can't go wrong. I have some slightly different variations, however, and here they are:
Section 1: First Studies
Etudes 1-8 - Here I play at a very mezzo dynamic and follow Mr. Alessi's advice of TONE CLONING. I am always striving in these to follow the KISS principle: Keep It Simple, Stupid! Anything that looks or sounds complicated, with unnecessary motion or turbulence in the sound anywhere, is almost definitely too complicated. The best brass players do the simplest things perfectly, cleanly, and simply, and here is your opportunity to practice the absolute simplest things every day.
Etudes 9 and 10 - I play these about mp, slurred as directed by Mr. Alessi. The KISS principle is extremely important here.
Etudes 11-15 - Now I diverge a bit from Mr. Alessi and Mr. Bowman. I play these rather loudly, about poco f, and I play them with legato air but marcato tongue. It's very important that you do not stop the sound! This requires moving the slide exactly in rhythm with the tongue, quickly and efficiently moving from one position to the next without bouncing or adjusting. It also requires keeping a consistent shape to the sound as you make articulations, helping to cultivate independence of the embouchure formation and articulation motion.
Etudes 16-25 - In both editions of Charlie Vernon's The Singing Trombone, he includes number 16, with the following instruction: "Do this exercise first without the tongue, smearing between each note (except where natural slurs occur)...The slower, the softer, the smoother, the BETTER!" That's how I do these. This is tiring if done right, so I always take a 2 or 3 minute break after this one.
Another aside: although many band directors and teachers make an absolute rule against tapping your foot while playing, many, if not most, of the great brass players I know often tap their feet when practicing. Charlie is a great example; his feet are going all the time, as a coordinating point for all the necessary physical motions to converge on. Things have to change in our bodies to get from one note to another, and everything is better if they change in a perfectly coordinated manner. Tapping your foot can be an extremely helpful way of timing in everything else that has to happen.
Etudes 26-40 - Here I make a couple of choices, depending on how I'm feeling. If I'm tight I might play one like 16-25, but faster and about mf, in order to counterbalance what I've just done. More often I play one of them like 11-15 (which I might have missed, depending on the day). Sometimes I instead put space between notes, focusing on consistent shape to the end of a note that is released and clear, consistent articulations after the spaces.
Etudes 41-45 I play fast, often double-tongue. Sometimes I play fairly soft and light, sometimes I work on playing fast and loud, but I'm always paying close attention to clear, consistent articulations.
Etude 46 is my favorite thing in the entire Arban's book, and I generally play it legato, at about mp. I am paying very close attention to pitch here, making sure every arpeggio sounds just right in its key, and again, I am striving for the simplest, most consistent transitions between notes. I am also listening intently to the tone quality, striving to keep it consistently rich, full and unforced.
Etudes 47-50 I generally play staccato but not at all pecky, striving for consistent articulations and note shapes.
Studies on Syncopation
Etudes 1-12 - These are excellent, and I use them to practice consistent articulations when combined with contrasting note lengths. Short notes before long notes are very short, and long notes go all the way to the next short note, with a very brief space, if any at all. The challenge is to make every articulation equally pointed and clear, regardless of how much space precedes it.
Studies on Dotted Eighth and Sixteenth Notes
Etudes 13-18 - One of my earliest and most influential teachers was Per Brevig, who insisted on the ability to play dotted rhythms with a perfect internal subdivision. I play these rather slowly, about 88, and don't let my 16th notes (later 32nds) be either triplety or snapped too close to the next note. I also make sure that there is no hint of ta-da to the articulation. These can be valid musical choices, but you have to have the ability to play the same articulation, regardless of the rhythmic figure.
Articulation and Style
Etudes 19-27 - Now we're getting into some music, and it's time to play musical phrases with great style, incorporating all the consistency of articulation and tone production we've been cultivating. Dr. Bowman and Mr. Alessi give great advice here. One bad habit to guard against often shows up right away in #19, with articulations that sound like Ta Ta-da-Da ta. Again, there are times when this is a good choice of articulation, but for this purpose we want to make sure we can play five identical articulations in the context of a musically shaped phrase. Ta Ta-ta-Ta Ta.
Etudes 28-31 are a good opportunity to give your musical imagination some permission to play, varying articulations as you hear the phrases. I often play #31 mostly legato, but you should make your own choices.
Etude 32 is great for practicing making the melody heard even while you have other, less important, notes to play around it.
Etudes 33-37 - I usually double-tongue the 16th notes, and if I am in good shape I play fairly fast in order to challenge the speed of my tongue.
Etude 38 I play very much like 13-18, but usually faster.
That's it! The first few times you do this it might take longer because you feel compelled to practice the difficulties that come up, but I recommend not dwelling too long on them. Do your best and move on. You don't have to solve every problem today. You will come back to the same issues tomorrow with a slightly different combination of notes, and you will see real and noticeable improvement, probably in less time than you thought you would. Remember, many of the fundamental skills we practice are actually quite a bit more difficult than most of the music we perform - which is why we do them!