Tutorials and examples are the fastest way (in my opinion) to learn a new language.
Well, ZX BASIC is not so new if you are used to Sinclair BASIC.
The following is a list of examples, some of them already bundled with
the ZX BASIC distribution in the
Draws a circle pixel by pixel using PLOT primitive
Sample clock which uses the FRAMES variable (taken from the ZX Spectrum 48K user manual)
Like above, but a bit improved.
Colors example from the ZX Spectrum user manual
Random color lines example from the ZX Spectrum 48K user manual.
Factorial ''recursive'' test.
A sound demo (taken from the ZX Spectrum 48K user manual)
UK Flag drawing (taken from the ZX Spectrum 48K / 128K user manual)
Mandelbrot fractal by @Britlion