Whether the moon will be of any help will depend on where it is and its phase. Checkout one of the many online sources for lunar data such as:
Complete Sun and Moon Data for One Day
SkyandTelescope.com - Sky Chart
The moon, like the sun, appears to move (its actually the Earth thats spinning) 15 degrees in one hour. This means that it will be only 15 degrees above the real horizon one hour after moonrise at the most. Depending on season, the wobble in the moon's orbit, and your latitude it may well be noticably lower. At middle and higher latitudes you generally can't rely on decent light from the moon untill 2-3 hours after moonrise and only until 2-3 hours before moonset. Where I live (Key West FL, USA) beaches are on the southeast of the island and moonlight is strong within minutes of moonrise and lasts until about 2 hours before moonset since the moon generally sets out of sight behind the building and trees inland from the beach. In winter, the moon is sometimes visible from some of the beaches from rise to set since its enought south to rise and set over the water from the beach's viewpoint.
A full moon or a waxing or waining gibbous moon can provide a decent amount of light provided its reasonably well above the visible horizon (trees, buildings, ...). You'll need a tripod as a rule but should be able to get some decent shots.
Don't rely on you camera's meter too much. Light levels will be low enough that no builtin meter will be particularily accruate and they might be well below the meter's range altogether. Take test shots and review the histogram if you're shooting digital; bracket well if shooting film.
You will likely be in low enough light that your camera's autofocus system, if it has one, won't work well or possibly won't work at all. Be prepared to focus manually.
Also, it is vitally important that you start the shooting with a completely full charge on your battery or new batteries if your camera uses expendable ones. Long time exposures eat batteries for lunch.