As a rule of thumb, under typical UK conditions you will need about 1 square metre (m2) of solar water heating panel area per person.
Acorss the year this should produce just over half of your domestic hot water (DHW) demand - the hot water needed for the bathroom and kitchen (see also: How much hot water can solar water heating produce?)
The 'flat plate' type of solar collector is usually between 2m2 and 4m2, so a typical house usually has either one or two of these panels.
If using an 'evacuated tube' collector, you may need an array of between 20 and 30 tubes to meet the hot water needs of your household.
The sizing of the panels and cylinder will be undertaken by the installer of the system, who will ask a few questions about your hot water use in order to design a system that will meet your needs.
The orientation of your roof will also be a factor - see 'is my home suitable for solar water heating' for more on this.