I doubt there's one "best" way, but I can share a couple of thoughts about how to practice the scale (or any scale). As with anything musical, you get the best results if you can fully engage with the material mentally, physically, and emotionally. So if you find yourself bored, take charge of your learning by changing your approach until you can regain your enthusiasm (breaks are good too).
These are suggestions and not a course of study so feel free to mix and match. I don't intend to suggest that you must do them all. They represent some ways of learning that I find rewarding, so I hope you do too. If you get one idea that helps you, then that's great!
1) Get or make 12 diagrams of the entire neck. Map out the dots for the scale in every key. It's not very hard if you know the order of the intervals, which you have to know to practice it anyway. Then start visualizing different paths through the dots, and play around until you find some nice melodies/licks.
2) Find a chord voicing you like, and using copies of your diagrams, circle the notes that make that voicing. Then, move all the voices of the chord up one scale degree, then another, until you have all seven chords in that particular family. Try that with as many voicings as you like. Also use 2 and 3 note chords; lots of times they sound better, depending on context. You can often leave out the bass note if there's a bassist.
3) (This should probably be #1) Make sure you know what your purpose is in wanting to have facility with this scale. If you have only a vague idea, try to find more about it's uses; knowledge builds excitement and confidence. You need to be in touch with your motivation to keep going until it's a permanant part of you. The most popular use of this scale in jazz is to play it's 7th mode over altered dominant chords. It's wonderful for that, as it contains all 4 tensions; the flatted and sharped versions of both the 5th and 9th! Really sounds cool! But explore lots of other uses too. There are other modes of the scale that also work over altered dominants; they just don't contain all 4 tensions; which might suit your mood better at times.
4) Make up tunes and chord progressions with it.
5) Don't get overwhelmed with all this stuff; take little steps and celebrate your progress. If you don't care to learn it in more than 1 key, that's one key more than the average shmo knows! Congratulate yourself, and don't beat yourself up because you aren't Joe Pass!
6) Try improvising over a 12 bar blues, combining blues scale riffs with altered dominant riffs. It sounds much better if the chords are played with at least one tension, an altered 5th or 9th-so there's some agreement between the chords and the solo.
7) Get familiar with all the intervals in the scale; try to learn to go up and down using harmonized 2nds, 3rds, 4ths....thru 13ths. Pay attention to their visual shapes, their feel, and sound.
8) Make little games out of it, like seeing if you can play some melodies on only the low E and A strings, then only the low E and D, etc. Try as many string groupings as you can, just 2 notes at a time so that you get more intimate with the intervallic relationships. Also spend time hanging out on the most unfamiliar area of the neck, until it feels like home. As much as possible, try to always break out of any ruts.
9) Try to play it in the context of songs as soon as possible.
10) Use it as a composing tool; create melodies and chord progressions based on it.
11) Once you know one pattern, add another, and another, until you know them and can connect them. Eventually you won't have to really think about it, and can just move freely in any direction.
12) Once you can connect the patterns, make sure you don't get in the habit of always changing position the same way (by sliding your little finger up on the G string, or whatever). If you find yourself in that type of rut, just come up with as many different routes as you can to the same destination, and spend most of your practice time on the routes that feel hardest.
13) As with anything in music, work on making as good a sound as possible for the least amount of effort. For example, if your hand gets tired, perhaps you're pressing much harder than needed to produce a clear tone. The goal is to get into an effortless flow; the zone we all want to be in. Of course you need a balance between effort and relaxation, but try to do everything with as little effort as possible.
I hope that helps and that it's not too daunting. If it feels like work, back off a notch until it's a fun adventure, as music should be.
