Being a musician means that you are constantly training your ear, brain, and body to work together to bring out the message of the music you play. Fingerings and note reading are just details; to make music, your SOUND must be the highest quality you can produce. Part of that dynamic (pardon the pun) is playing in tune. Even many untrained listeners can distinguish between flat and sharp pitches, and so should you!
While it is important to assemble your flute in such a way that it is roughly in tune with itself, it is even more important to play in tune. Learning to do this takes years of practice for some students; however, a chromatic tuner can help develop this skill.
For the ensemble player, playing in tune is important for blending with other musicians' pitches. Sometimes an ensemble may not be perfectly in tune, but the group can still produce a pleasing sound if the members are in tune with each other.
For the soloist, it is tantamount to good musicianship to learn to play in tune by hearing yourself play in tune. Just as using a metronome helps develop your internal rhythmic steadiness, using a tuner helps a student recognize correct pitches.
An excellent teacher will introduce the use of a tuner relatively soon after the student has begun lessons. Good teachers know the value of ear training and will constantly seek to develop that skill in students.
How-to: The Nitty-gritty
*At the first of each practice session, warm up your flute by playing some slow scales.
*Turn the tuner on and play an "A". (Theoretically, you could play any note and a chromatic tuner would respond correctly; however, "A" in the staff is the standard orchestral tuning note.) Play your note the way you always play--not softer, not louder, not harder--just plain. Let the tuner tell you what it reads. The needle may indicate flatness; if so, make the tube shorter by pushing in the head joint slightly. Conversely, if the tuner indicates sharpness, lengthen the tube by extending the head joint outward. Repeat this experiment until the tuner registers a correct pitch (at A=440). At this stage, it is important to not force the tuner to read the way you want it to by making your pitch match by manipulation. Instead, let the tuner do it's job, giving you a true reading so you can make adjustments.
*Next, play an "A" above the staff. This time, since your flute is already in tune in the lower register, you will be checking to adjust yourself (air speed, position, embouchure) to play in tune.
Just because your flute is in tune does not necessarily mean you will be playing every note in your piece on a correct pitch. Notes in the third register are particularly problematic, and each flute may respond differently to various notes. Use a tuner during your practice session to check the tendency of problematic notes. Is your high Eb generally sharp? Learn to adjust your embouchure to keep it in balance.
The tuner that's right for you
Many of my students enjoy using a combination metronome tuner such as the Korg TM-50. However, if you already have a metronome OR you like having a separate tuner, the Korg CA-40 would work well for you. There are several reliable brands, however, such as Sabine, Seiko, and Fender. A good tuner is indispensable and should last you for many years (as long as you don't drop it too often).