Flight Manual:
1) Activate Stability assist, go full throttle and press 9
to activate the engine.
2) Wait for the engine to rev up a bit and press spacebar for staging
3) Press spacebar again to get rid of the rocket.
4) You are flying
Real photograph taken from Wikipedia. Original author here:
https://www.flickr.com/photos/sdasmarchives/4559138005/in/photostream
A stock aircraft called F84 ZELL (Zero-Lenght Launch). Built with 25 of the finest parts, its root part is Mark2Cockpit.
Built in the SPH in KSP version 1.12.2.