remove as many of the leaves from the stems as possible. Tie three or four stems together using sewing cotton and hang upside down in a dark, dry , warm place. The flowers will take between a week and three weeks to thoroughly dry. There may be some fading of the flowers in this process, but that can actually look really nice.
The flowers shown in the first picture are Helichrysum and are paper like in structure. They hold their shape and colour. (pick them before the centre of the flower develops)
flowers that work really well for drying include
Larkspur - blues, pinks and white
Nigella - green seed heads
Opium poppies - blue/grey seed heads
Amaranthus - dark red, green or 'biscuit'
Statice - blue, pink, yellow and white