When picture-postcards were first sent out in the 19th century they were the Victorian equivalent of today's text message - pithy, informal, to the point.
There is little etiquette surrounding postcards: you do not normally have to start them with a salutation (you can go straight into the message), and you do not need to employ any particular sign-off. They form a verbal snapshot: a message from a particular place (most typically a holiday location); or simply a reminder that you are thinking of a person.
A range of postcard clichés is available: 'wish you were here'; 'having a lovely time'; 'we saw this and thought of you'. If possible, eschew the obvious, and inject your postcard with personality - a humorous observation or a personal reference that proves you're actually thinking of the recipient.