I would say it's a matter of degree, and what the heck, that's what phonemes are for. :) Japanese has no English "f" or “v" proper, so to get them there (particularly, the kids), I had them exaggeratedly put their upper teeth well out over the lower lip so they could hear what they were aiming for. As they got more proficient at it, they could bring the teeth in behind the lower lip to get the same sound in a position more conducive to allegro speech and look less like they were having a seizure. So, too, with ð and θ. If you don't feel you've mastered them yet, go a little over the top for a while and use the exaggerated tongue-between-the-teeth approach. As you get comfy with the sound, you can play with the tongue behind the incisors to achieve the same effect (and again, that'll be easier for speaking allegro). (And if you want to play around with regional variants, go with God :D ) It's like whistling. I can whistle by puckering up and blowing; I can whistle by using my tongue apically against the alveolar ridge. There's more than one way to skin a cat. ;)

Neil gave a great answer. The sound is called by linguists a bilabial fricative. I was always taught to "try to bite my tongue" when making the sound.

It varies a lot actually geographically. I am from Ireland, and we are known for a distinctive hardening of the ð, almost omitting the h. We place the tongue at the back of the incisors, just below the base of the alveolar ridge. But it is considered lazy by speakers not from our country :) Definitely there is a correct way to pronounce both. I think the ð (as in This, That, These and Those) have an occluded start - the breath must be almost completely stopped by the tongue at the beginning of the sound, and then released at the end of the sound to generate the 't' sound. The θ (as in with, froth, has almost no stopping of breath - it is almost a constant, but restricted passage of air that is close to an elongated 's'. I think the correct method is always with the tip of your tongue below the tip of your upper incisors. There is a rhyme which is used to practice this: "This, That, These and Those - that's the way the T H goes - With the tip of the tongue between the teeth, This, That, These and Those!

I make my students bite their tongues properly, even if it seems weird to them. If they keep the tongue behind the teeth, then they resort to using t/d/s/z. It's definitely possible to get the fricative from behind the teeth, but biting the tongue is a guaranteed result.