For those saxophonists who plan to make playing music their profession, playing several woodwinds is eventually a necessity in order to keep yourself in supply of enough work. There is also much to gain out of what you learn by playing other woodwinds that can augment your saxophone playing.
There are a few things that are good to remember when considering doubling. First of all, every woodwind is a different animal. What do I mean by that? Well, you can't take the approach that just because another instrument uses the Boehm fingering system that "you already know it" and that "it will be easy". Far from it! Every instrument has its own character, nuances and history that accompanies it - and its own problems. Even if you double on another saxophone say, alto and tenor, or tenor and soprano - you have to treat them as though they are totally different instruments in order to get the most out of them. The basic essential woodwinds to play besides other saxophones are the clarinet and the flute. Other instruments beyond that would be the oboe and English horn.
How do you go about starting to learn to play another instrument? First of all, you need to allot time to dedicate practicing this new "friend". That's right. You have to get friendly with the instrument and see it as something to help you and not make your life difficult. If you review the first newsletter you've received - "Mastering Basic Skills" - this will help you get clear on how well you should learn how to play this new instrument. You need to develop a good tone, good intonation and a decent technique. You must investigate music composed for the instrument and get some solo recordings of the instrument in order to form an idea of what is possible with the instrument and what sound you may want to acquire. And of course, very good sight-reading skills on all instruments.
Depending on the type of professional situation you may be involved in will more or less dictate how proficient on each instrument you should become. For example, if you're planning to play musicals, most of the time, the saxophone is going to be the least important instrument in your arsenal. The first reed book of the musical "A Chorus Line" demands good flute and piccolo proficiency, a little clarinet and very little saxophone is needed. "West Side Story" needs advanced clarinet proficiency. "Grease" needs mainly saxophone with a good grasp of playing different musical styles and some clarinet good clarinet skills. Musicals like "Bubblin' Brown Sugar", "Eubie", "Ain't Misbehavin'" need good skills in interpretation of sax and clarinet playing styles of the swing era.
What if that's not your goal? Studio musicians need to be proficient in many styles, on cue (!) and be particularly a master of at least one style. Show bands or Club Date bands also need a good grasp of various styles and various instruments. Whatever your genre you have to know in and out.
Sax/Clarinet double - here you need a lot of work on your embouchure and your reading skills. Clarinet is not built in octaves like the sax, so you'll have learn practically a different fingering for every note and you need to drill reading the notes far below and above the staff. Watch that vibrato! If you use it on sax, you need to get rid of it on clarinet (in the meantime).
Sax/Flute double - here you'll also need a lot of embouchure work and reading skills. For flute you'll need to practice overtones often and work on projection (getting heard)!
Sax/Clarinet/Flute double - You need to practice switching between these instruments for quick embouchure adjustments and reading.
Along with doubling on clarinet or flute, you may need to investigate other voices of those instruments such as bass clarinet, basset horn, piccolo and alto flute. If you add oboe to your arsenal, you may also need English horn too. With whatever doubles you have I suggest dedicating one hour (at least) a day (every day!) to practicing the instrument(s). You'll be amazed what you can achieve after 6 months! In that time, you'll also learn to develop a "feel" for the instrument so that once you touch it, you'll trigger off messages in your brain that will dictate to your fingers, embouchure and ear as to how and what to do. You'll recognize the "new animal" instantly.
Get together with other doublers to play duets, trios or quartets with your doubles. Help and support each other in learning. This is also an important lesson in "networking". Letting others know that you play doubles for future reference. A lucrative gig may come out of it. And don't forget to offer then gigs when you have a chance to also.