There is no standard format. Plain english is good, just make sure you put any constraints together up front too. What I like to do is give pre-conditions, communication points, actions, errors and goal of each page I think I need -- and tell them to feel free to challenge or adjust as needed. This gives them basic data points of what your goals are per page, and the pre/post conditions tell them how to get to the goal of the page in the least number of steps and what designs might be best. Also, if you know you have a data structure you have to present that is complex and would work best in a certain style of control, tell them that up front so they can design around it. This can make a major difference in time to market.
And as new_guy said, always point them toward a few different apps/websites you like the design for so they can get a feel for the design.
Also, if you have a color pallet give it to them early, like if you have any brand standards etc, then they can incorporate that all up front. I have had many designers on my staff over the years and this is a major sticking point for them when clients would give us projects. It sounds stupid, but sometimes you can't just change the color in a design and have it look right, it requires a different layout etc. So just be up front if there is something to avoid or something you really want.