Could you help me to do a syntax analysis of this sentence?

This is a parallel comparative. It shows up in a lot of languages:

Plus ça change, plus c'est la même chose. [French: The more things change, the more they stay the same.]

Je größer desto besser [German: The bigger the better.]

If you were to express this mathematically, it would be something like:

a + n ~= b + n

where a, b, and n are positive numbers.

It's a common way of expressing how two things are related from an experiential perspective. In your example, the sentence expresses that using Froyo (currently, the latest Android operating system for smart phones) is a very rich experience, and the speaker learns something new practically upon every encounter with it. It is here used to express approval of the new OS.

More positive examples:

The more I get to know you, the more I like you. [The speaker's relationship with "you" is growing in a positive direction.]

The more I see Fellini films, the more I understand how film can be used expressively. [The speaker has learned a lot about movie-making from watching Fellini.]

It doesn't have to be an approving comment, however. Here are some negative examples:

The more I eat liver, the more I like steak. [In other words, the speaker really doesn't like liver.]

The more I go to class, the more bored I get. [The speaker really doesn't like going to class.]

No, it means the amount of 'new stuff' you discover increases the more 'Froyo' is used.

I more use Froyo, I discover more new stuff.

Makes no sense I'm afraid.

The sentence can be rephrased to:

If I use Froyo more, then I discover more new stuff.

This is sort of a logical rephrasing, without any subjective emphasis in it. The original puts more emphasis on how useful doing the first action is.

Mathematically, this is expressed that the second thing is proportional to the first, or that the second linearly (as opposed to, say, logarithmically) increases with the first: b ~ a * x. So if x is 2, meaning that I double my efforts in doing a, then b will also double. If I use Froyo twice as much as I do it now, I will learn twice as many new things.

It also emphasizes that the experience continues to be fruitful to me. The benefits won't decrease in time, which is to say that I won't reach a point where using Froyo as much, I will not learn anymore, because I've learnt everything. I always learn more and more, in direct correspondence to how much I use it. Of course, this might not be true in real life, but phrasing it this way, I point out how very useful using Froyo is to me.