Tip of the tongue for "L"

My accent instructor (for American English) told me that my "L" sound is too throaty and weak, whereas it needs to be crisp, sharp, and clear. The way to achieve this is to press the "very tip" (her words) of the tongue against the back of the front teeth or the roof of the mouth near the teeth.

What I'm not clear on is "the tip of the tongue." The tongue doesn't have a sharp point, it's a curve. What I can do is press the "upper part" of that curve at the front against the back of the front teeth; i.e. arch my tongue and raise the small frontal part of the curve against the front teeth. This is not a sharp point, but still a curvature. Is this correct?

The way I curl my tongue here is similar to the way I curl it for "R" (but of course, it's not as curled and forward of the "R").

Is this description of the "L" correct--an arch of the back part of the tongue, while the small frontal part touches the roof of the mouth behind the front teeth?

Thanks

L can be pronounced dark (velar) in many American accents, even in initial position. No need to change that.

As Kaeops observed, /l/ has a wide range of realizations in American English. The textbook realization has [l] (purely alveolar, made with the tip of the tongue) in syllable-initial position and [ɫ] (similar, but velarized) in syllable-final positions; more progressive realizations might use something like [ʟ] or [ɰ], with no alveolar contact at all. (Are you familiar with IPA? If not, see http://en.wikipedia.org/wiki/International_Phonetic_Alphabet .)

<<What I'm not clear on is "the tip of the tongue." The tongue doesn't have a sharp point, it's a curve. What I can do is press the "upper part" of that curve at the front against the back of the front teeth; i.e. arch my tongue and raise the small frontal part of the curve against the front teeth. This is not a sharp point, but still a curvature. Is this correct?>>

You have the mechanics correct, but not the terminology. The front part of the tongue is referred to as the apex or tip, and consonants made with the tip of the tongue are referred to as "apical" (as opposed to laminal consonants, which are made with the flat part of the tongue). Just because it's not perfectly sharp doesn't mean we can't refer to it as the tip.

Actually, I would say that having a pure "light" /l/, that is, [l] with no coarticulation at all, in all positions would sound like a non-native accent in what is otherwise North American English.