India's "space shuttle Avatar - will launch from a rocket initially to test re-entry but once re-entry is perfected will launch from an ordinary airport.
The problem with going to orbit from the surface is the high delta v needed of about 9.4 km / second.
If you use a vertical launch rocket then you can carry all the fuel in separate stages that you discard on the way up. Typically there are three stages - the first two fall to the ground, and the final third stage goes into orbit along with your spacecraft and then burns up a few orbits later, typically.
The Skylon and Avatar are regarded as Single-stage-to-orbit, because no hardware is discarded at all on the way up.
They would achieve that because they are air breathing so can get oxygen from the atmosphere on the way up. The main problem with this, the reason most rockets don't attempt it, is because the air enters at such high speeds and is at high temperatures. Skylon has an innovative engine that can cool down the incoming hot air to well sub zero temperatures in a fraction of a second. They have proved that it works in tests on the ground and the project is still going ahead.
Both of these projects, if they come to fruition, are for some time in the future, maybe in the 2020s.
For some other ideas of ways to get to orbit without needing to use multi-stage rocket systems, see