To is a preposition. We know that because the other to in English, the infinitive marker to, only takes base verbs; e.g., to be, to go, to run, to eat, and so on. So, infinitive to never takes and cannot take an inflected form; e.g., -ing.
Originally Posted by Tvita
Now, the word speaking carries -ing, inflection, which is a telltale sign of a verb, but it isn't a verb. We know that because words that end in -ing if they are a verb are part of a bigger verb, the present progressive, also called the present continuous, and that looks like this: BE + -ing, e.g., am speaking, is speaking, was speaking, were speaking, and so on. If speaking were a verb in our example key to speaking, then it would need to co-occur with a form of the verb BE (am, is, was, were, etc), but it doesn't, so it's not a verb.
Speaking is a noun, also known as a gerund. Gerunds look like verbs, but they aren't verbs, because they don't co-occur with a form of the verb BE. Gerunds are verbal nouns and so they function like nouns, and like verbs. As verbals they can take objects. Below, the gerund speaking takes the noun English as its object:
...speaking English <object of the gerund>and gerunds can also be modified by adverbs. Below, the adverbs easily and fast modify the gerund speaking English:
...to speaking English easily, and fast. <adverbial modifiers>As nouns, gerunds sit in object and subject positions.
...key to speaking English easily, and fast. <object>Going back now to the preposition to, a preposition needs an object, and it takes a noun as its object. In our example, the gerund speaking English is the object of the preposition to.
Does that help?