It appeared to me that they just absorbed into the human bodies. And there was one alien in the series trapped in a human body since the invasion of 53, so it is their own natural ability to merge into human bodies.
I played around with some of the things you could assume about alien biology from what we know from the series in the Memory story I wrote.
First of all, the chances of them having anything like DNA/RNA as their genetic material is pretty much nil. That would be a coincidence to end all coincidences. Unless we're assuming that the aliens are somehow an offshoot of Earth life, which leads to all kinds of interesting plots - and it does make sense, if Earth (sans humans) is their idea of a paradise, as they say now and then.
However, it also makes sense that they don't use anything like DNA. They are, after all, resistant to radiation! So maybe they are entirely small-molecule-based. That would nicely explain why they're not susceptible to radiation damage, and would be a floopy hand-wavy way to get into the takeover of bodies. They can mimic our second messengers.
It doesn't explain how they can have all of the information needed to pattern a living being using only small molecules. I had this idea that they had a small-molecule-based system to control ion flux - that would give a way to link the aliens to the action potentials in human brains.