[susan53]

I would argue that it functions as a subordinating conjunction. You can see this easily if you parallel it with other subordinating conjunctions such as that or if. To do so, I've had to change the context slightly, but the sentence construction remains the same. :

He told me that he would do it.
He told me how he would do it.

I don't know if this machine works.
I don't know how this machine works.

You can see from these two examples that how is acting in exactly the same way as that and if to join the two clauses. Hence, for me, it's a subordinating conjunction.

However, the Cobuild Dictionary, while classing how as a subordinating conjunction in sentences like Tell me how to get there and This is how I make a vegetable curry, has them as adverbs in Do you remember how you and I planned to live in Venice? I'm not completely sure of their reasoning here - I don't see the differences between the two groups. Again, in the last example how could be replaced grammatically with if or that.

The Grammar of Contemporary English (Quirk et al, Longman 1971) hedges its bets by suggesting that interrogative words such as where, when, how (which of course do act as adverbs in sentences such as How did you do it?), in this type of sentence can be seen as a blend of both adverb (or more technically pro-adjunct) and subordinating conjunction - ie a bit of both. This makes sense to me, but if I had to argue for one or the other, then - subordinating conjunction.