I have played drums for a few months. Currently, I play for myself. I do exercises from stick control, but I also want to 'play along' to songs.
Given a song A, how do I start playing along? By ear? Make a sketch of its basic time signature?
There are a few different levels here. One of the things you can practice are "Grooves", for example, those included with the Vic Firth Groove Essentials packages. That will give you some starting places based on the style of the music, and it's a lot easier to learn from written-out grooves than to decode every little thing by ear.
You'll also need to figure out the overall form of the song. If you "know" the song already, say, you know exactly how it goes and might be able to sing along, you probably already have a concept of the form. This might be something like:
4-bar intro, 32-bar A section, 8-bar bridge, 32-bar B section, end
It doesn't have to be formalized like that, but if you're having trouble figuring out the large-scale structure of a song, it can help to put it down in writing. You might have a slightly different groove for each section, or not--use your ears to figure out what changes.
If you can play some relevant grooves and you know the song form, that should be enough to get you started. Depending on how complicated the song is, transitions between sections might take a little more work.
A large part of drumset playing in certain styles of music is improvisational, so training your ear by learning drumset grooves by ear or transcribing them can be very useful.
Now, another approach to this is to find books of drumset parts that have been transcribed by a professional. These are often published for the express purpose of having people buy them to play along with the songs, and often include a recording or remix with the drums subtracted.
One very neat trick a teacher of mine taught me is to start transcribing a new song using personal symbols for each part. For example: a dot for every bar of the Intro, then a square for the Verse, and a triangle for the Chorus. It's a very quick way for start grasping the overall structure, however with more complex songs you can start putting little modifiers on each symbol. E.g.: a triangle with one stripe for the first verse, and then a triangle with two stripes for the second Verse because it's the same groove but a little different.
This modifier idea is nice because you can recognize that even when the groove has some differences, the overall idea is pretty much the same - and afterwards you may want to add your own little nuances to that.
Then, you begin learning how to write sheet music for drums (which is very helpful, and I recommend a lot!), you can complement that early notation with a little "dictionary" thing where you explain on a footnote the meaning of each symbol.
Of course it's a very simple technique for writing music, which is quicker than writing a whole sheet music, but has less "expression power" than that. You'll find that there's always a trade-off, and sometimes one will be more appropriate than the other.