The thread topic is programs for learning Thai language, but allthai has posted about the wai gesture, so I'll follow him, and several others, off topic.

That quote above sounds good at first glance, but my personal observations and experiences show it's often not true.
And that can cause embarrassment -- which is the last thing you want to happen with Thai people.

In over two years of living in Thailand, I have only waied twice.
That was enough to learn that the wrong wai, in the wrong situation, can be highly upsetting to some Thais.
I will explain as a warning to others.

I had spent several Saturday afternoons helping teenage children of a family next door practice English for an end of term test.
I'm not an English teacher -- refused to accept any money -- just being friendly to neighbors.
After the last practice session, the two teenagers brought me a very nice gift.
I said, "Thank you", and I gave them a very restrained and modest wai, not a deep wai.
They instantly became very upset, shocked looks on both faces, and the teenage boy blurted out, "Khun Peter4, you must never do like this to us!"
When I gently asked why not, the boy couldn't get out any words to explain, he just stuttered.
Apparently it was such a social gaff that it was beyond words for him.
Then his older sister, in a very hushed voice, explained, "Because we are children and you are pu-yaay (adult with high status).
So, my modest wai of thanks was certainly not acceptable to those Thais.

Second experience came with another family in the neighborhood.
There, too, I'd helped teenage son review English for college entrance test.
After the test, mother and son brought me a very nice gift.
This occurred in the lobby of my condo, with, perhaps, a dozen other Thai people coming and going in the lobby at the time.
Again, I gave them a modest wai.
Again, looks of shock.
The mother and son quickly turned away and almost ran out the door.
They did not even stop to return my wai; they just fled.
Certainly not acceptable to those Thais.

Later, I explained about this to my Thai language teacher.
As my story unfolded, my teacher got a somewhat horrified look on his face.
He knows the mother, and he knows she is a maid in a hotel.
The boy is 17.
In the hierarchy of Thailand, I am far, far, above them in status.
When I finished describing the details of that wai experience, he sat back, paused a long time -- as Thais often do when embarrassed -- and then said, "Khun Peter4, perhaps it is best if you don't wai until I teach you about this. There are many things you must know first."
Since then, he has never offered to teach anything about the wai.
But here, on this forum, some foreigners are eagerly encouraging other foreigners to wai.

Since those learning experiences, I have made it a point to observe other foreigners and tourists here, and when they wai, instead of watching them, I watch the faces of the Thais who are on the receiving end.
There are many different kinds of smiles in Thailand.
What I've seen on the faces of the Thais, in many cases, is best described as a "smile of embarrassment"; somewhat of a cringe.

For the short term visitor here -- such as the OP -- I don't see where a few words of language or a wai will be useful to you.
When my friends come to visit, I always advise, "Just smile."
In Thailand, a simple smile is always welcome.
And simple English, spoken slowly and distinctly, is far more welcome than half-baked attempts at Thai language.

-- Peter