I've been wondering...is it even possible to have an SSTO that doesn't have wings?
And, perhaps more importantly, does anyone have advice on how to get SSTO spaceplanes to orbit?
As I said, with the new parts in the ARM pack, it's pretty easy.
To make SSTO spaceplanes, you need either Turbojets or RAPIERs, plus the ram-air intakes (the glowy blue ones). Get a decent takeoff TWR, add enough wings to glide with the tanks full, and set up some action groups to quickly toggle your air intakes and engines.
When you have that, you take off, aim 45 degrees upwards, get to 15k altitude and accelerate as fast as you can while staying in the atmosphere for as long as you can. Open the resource panel and watch your Intake Air level, do not let it drop fully. At some point you will likely need to be accelerating almost horizontally, building speed while almost not gaining altitude at all, but it's important that you don't start losing altitude because denser air will slow you down.
At some point your intakes won't get enough air. The exact point where that happens varies, but you should be at at least 20-24km altitude and going at 1000 - 1300m/s, otherwise you're unlikely to make orbit. If you have a turbojet, now is the time to fire the rocket engine(s) and toggle the jet and the intakes off via action group. If you have a RAPIER, it will switch automatically, so you only have to close the intakes. On rocket power, you aim up 45 to 60 degrees, open the map screen, and do your best to push your apoapsis to space, higher is better. Once you think you're good, coast to the apoapsis and, if you still have fuel left, circularize.