By e-mail, face to face or just give him/ her a card.
If you wish to write an email to a friend inviting her to go to the beach (or anywhere else for that matter), then all you have to do is be polite, highlight the reasons you're going to have a great time, and throw in some ideas of things you will do at the beach for good measure.
Try to focus your letter on things she will enjoy at the beach: Here are some examples:
1. Hunky guys
3. Eating ice-cream
5. Building a sandcastle
I recently went to the beach with my friends, here's a YouTube video we made. Maybe you guys could do the same thing?