I am a first semester math PhD student who needs to transfer to a different school: how should I talk about my current program on applications?
While the notion of "transferring" has genuine substance for undergrad programs, and in many cases can be accomplished easily or even automatically, graduate programs work differently, certainly in the U.S. That is, operationally, there simply is no notion of "transfer" beyond applying to the program on an equal footing with everyone else. That is, the fact that you were admitted to one program does not guarantee anything about subsequent admission to some other program.

Even though grades will not be available by the application deadline, you can have them sent when they are available. Often the admissions committees don't really look at applications until (e.g.) January even when deadelines are in early December. 

You'll also definitely want letters of recommendation from the graduate program you're in now, in part to allay potential suspicions that things were going badly for you so that you needed/wanted a fresh start.

In particular, such applications routinely require transcripts from all previous institutions, and this would include the place you've just begun the program.