I assume you mean that the decking boards are rotten. This may also indicate that the support joists are rotten as well. If the deck joists are the extended floor joists you will have to determine if the rot extends into the interior of your home. If so you will have a problem you should call a qualified builder to repair. If not, you have the opportunity to head off this situation and make repairs so that this situation will not happen again.
You should remove all decking and joists for starters and make needed repairs to house joists and siding. A search for decking details will give you the needed information on current methods for construction of hanging decks. Your local building codes may have particular methods for attachment of new joists to exterior walls.
Plan, organize, be safe, and have fun.

Don't make the mistake of rebuilding without one. It will almost certainly come back and bite you one the ass.

The permit will require plans to be drawn up, and that may require an architect. That all sounds rather costly, but two words in your post suggest that cutting costs would be a very bad idea, "second story."