I run Workshops and Demonstrations around the art groups in the Liverpool / Manchester area, and I'm sometimes asked to "invent" a painting there and then; its not as difficult as it sounds.
Try this; depending upon you medium (Watercolour / Acrylic, etc.);
Make a mark of a fine line about one third of the way up the paper / canvas, and use this as your horizon line.
Next, paint in the sky, either wetting first and dropping colours wet into wet if watercolour, or paint the sky in Acrylic using a mixture of Cobalt Blue and White. Whilst the paint is still wet, make a few marks for clouds.
Next, Using the sky colour, add a touch of Alizarin Crimson to make the sky colour very slightly Purple, and paint in some undulating hills, not too even, with perhaps a bigger one to one side of the centre, and pulling the colour down just a short way under the horizon.
Next, mix a little Cobalt Blue with Lemon Yellow, and touch in some very basic shapes which could be single trees, or part of a forest; add little touches of Yellow and Blue to vary the green.
Next, With a stronger mix of the Cobalt Blue and Lemon yellow, brush in some green fields in the foreground, with touches of Alizarin Crimson, to darken the green in random patches.
Now stand back and look at your painting and think "what else would I like to have in this painting", and you are on your way to "inventing" your own composition!
Lets know how you get on if you try this, and go from there!
Very best wishes and good luck,
PA and RSC Wigan / Warrington / St Helens