If you do an online search for this topic, you will find lots of advice from teachers to keep the tip of the tongue by the bottom teeth. The reasoning is that it will prevent your tongue from pulling back into your throat and creating a "swallowed" sound. If someone were to ask me about this topic, my response would be, "It depends."
For those of you who prefer video format as opposed to text, I have addressed this topic in the YouTube video below. Otherwise, keep reading below.
There are four major variables that influence tongue position which I will be outlining below. They are: (1) tongue size vs. jaw size, (2) the vowel, (3) pitch range, and (4) sound color.
Tongue size vs. jaw size
The biggest factor that determines whether the tip of your tongue will be by your bottom teeth is the size of your jaw in relation to the size of your tongue. As a generalization, if you have a relatively small mouth, the tip of your tongue will likely often rest by the bottom teeth; on the other hand, if you have a large mouth especially if it opens a lot vertically, the tip of the tongue may "float" in the mouth more often. In this latter case, trying to keep the tip of the tongue by the bottom teeth can actually impair your ability to open your mouth! There are exceptions to these generalizations since we all come in so many different shapes and sizes, but these "rules" do hold true in many cases.
The tip of the tongue often falls closer to the bottom teeth on low vowels like AH and AA and floats more in the mouth for high vowels like EE and OO. The vowel is primarily formed by the MIDDLE portion of the tongue, so what the tip of the tongue is doing will often be irrelevant. To experience what the middle portion of the tongue feels like, do a siren on an NG sound. If you look in front of a mirror, the tip of your tongue will likely be floating in your mouth while the middle portion of the tongue will be arched high and helping to shape the resonance. While every vowel won't feel exactly like this NG set up, it does point you in the direction.
The higher you go in pitch, the more the mouth has to open. As the mouth opens more, especially if you have a mouth that opens a lot vertically, the tip of the tongue will tend to "float" in the mouth more frequently.
The more twang you bring into the sound, the more the tongue will tend to float since the tongue has to couple with the back of the throat in a particular way to create the resonance. This tend to happen the higher you go into your pitch range since more twang naturally has to come up for your upper notes, otherwise you will impair your range. If you want to learn more about how twang influences tongue position, look at the Edge mode in Complete Vocal Technique. Also, the more you open the mouth horizontally as for a smile, the more the tip of the tongue tends to rest by the bottom teeth; when you open more vertically, the tongue will tend to float more.
So what does all of this mean for me as a singer?
It means don't worry about your tongue position and instead, just simply focus on trying to pronounce your vowel sounds as clearly as you can while still keeping the throat supple. If you follow this idea, the tongue will position itself however it needs to for the given pitch, vowel, and sound color.
I leave you with some examples of singers whose tongue tip does not always lie by the bottom teeth. If you have questions, feel free to ask. For future updates, be sure to like the Vocal Liberation FaceBook page.
http://www.facebook.com/VocalLiberation Guy Penrod
Guy Penrod of the Gaither Vocal Band has a rather large mouth that opens a lot vertically. The tip of his tongue is often not near his bottom teeth as a result, especially in his higher range. In this video of Guy singing "Let Freedom Ring", look at his tongue from 3:55-4:01, on the "key" at 5:08, and "let" at 6:02. Note that even though the tip of the tongue isn't by the bottom teeth, the middle portion of the tongue is still arched just like every other singer on the stage.
Michael is an example of someone with a larger than average mouth which opens a lot in the vertical direction. As a result, he often displays a floating tongue, especially on his EH and EE vowels. In this live performance of "Anthem", from 2:46 until the end of the clip, you can often see a floating tongue. In particular look at "where" at 2:54, "let" at 3:00, "tear themselves" at 3:04, and "my land's" at 3:11.
Although Taylor has a mouth which is only slightly larger than average, her voice naturally has a lot of twang. As a result, her tongue is often in a high, arched position near the upper molars. When you combine this with the fact that the front portion of her tongue is short, you will often witness a floating tongue in her for many of her vowels. In this live performance of "Love Will Lead You Back", you can see the floating tongue on "together" at 0:35, "back" at 2:03, "long" at 2:26, and "back" at 2:30-2:33.
Yolanda has a very big mouth that opens a lot vertically. Like the other singers, you can see the characteristic arch in the middle portion of the tongue, especially on her EE, EH, and AA vowels. Her tongue often floats for her EE vowel in particular, which can be seen in this performance of "Imagine" from 0:38-0:40 when she sings "peace".
John Raitt has the combination of a small mouth with a short tongue. You can often see his tongue floating in his mouth for many vowels, including his AH. In this stage performance of "If I Loved You", you can see this tongue position. The song begins at 9:00. Highlighted point include "how I" at 9:04, "exactly" at 9:08, "how I'd" at 9:11, and "I" at 9:17 for examples on AH and AA.
Fritz is an interesting case because even though he has a small mouth, his tongue itself is actually short relative to the size of his mouth. So his tongue is often floating in spite of his small mouth size. Look at this video of him singing Tamino's aria. In particular, look from 0:45-0:55, 2:01-2:09, and 2:59-3:06.
Piotr is an example of a singer with a larger than average mouth that opens a lot vertically, very similarly to Guy's mouth. (You can't quite tell just how big his mouth is from this clip, but the size of his mouth can be seen more clearly in other clips.) In this montage of him singing song by Richard Tauber, you can see his tongue. In particular, look at 0:50-1:08, 3:21-3:30, and 4:01-4:07.
Mario del Monaco
Mario has an average sized mouth, but for his EH and EE vowels, you will often see the tip of the tongue floating in the mouth. In this performance of "Vesti la giubba", you can see his tongue floating for the EH vowel at 1:09. It is often floating in many other phrases in the aria, but it is most clear at that time.
Lauritz is a great example of someone with a small mouth but also a short tongue. Look at his performance of "Because" to see examples of this floating tongue. Especially pay attention to his EE vowels. From 0:51 to 1:20, there are good close ups of his mouth, in particular, the "me" at 1:16.
Giovanni is yet another example of the small mouth, short tongue combo. His tongue can often be seen floating in his mouth in this performance of "Torna a Surriento". Be sure to pay attention at 0:13, 0:46-0:56, 1:13, and 1:26-1:35.