The first thing to do is call your local FAA office. While these guys and gals may not be that experience in balloon building, they know all the paperwork you have to do. It is best to start out doing the paperwork from the beginning.
For some of the best homebuilding information, purchase back issues of the Balloon Builders Journal.
You can buy back issues for $2 each. I recommend buying them! The price for this journal is very cheap compared to the information contained within.
The Balloon Builders Journal
Don Piccard is filled with information on building balloons. You might wish to e-mail him with details of your plan to build. I would recommend doing this before you actually start, because he excels in balloon design.
If you want to design your own balloon, you can get the dimensions from Bob Nungester's program available at: http://www.jps.net/chuck1/empty_pockets.htm. I used this program myself. The spreadsheet I used to calculate panel sizes can be downloaded here. I would actually recommend getting ahold of Don Piccard and using curved panels instead of the straight ones that I used.
Another way to get panel dimensions is to use the gore pattern worksheet, available in Excel from here.
For fabric, I would recommend calling Julie at Westmark. They have good fabric, and they are one of the few people that will knowingly sell to homebuilders. Julie is pretty good, she remembered me when I called back a year later to order more fabric. You can request a free packet with fabric samples and colors. I'm sure it costs a fair bit of money to put together, so please only do it if you are serious about buying fabric from them. Here is the contact information for them:
For thread, I used "Dabond/Dashu(r)D" polyester thread from Heminway & Bartlett Co on Mason Street in Greenwich, Conn. I used two sizes, one was V-138, and I've lost record of the other. The thicker one I used to sew the load tape onto the panels. The rest was done with a slightly thinner thread.
For load tapes, you might want to look at Bally Ribbon Mills. I bought my stuff from Don Piccard, so I don't actually have any experience with them. They do have a nice free packet of information.
Bally Ribbon Mills
To sew a balloon, you need an industrial double needle sewing machine with a 1/2 to 3/8" gauge. 3/8" is preferred. These industrial machines are not cheap, but you'll ruin a home machine if you try to create a balloon. One site you can look at for machines is http://www.sewserg.com/. I have not ordered from them or talked to them, but they have several industrial machines listed on their site. If you want more info on selecting a machine, contact Bob LeDoux and ask for the two BBJ issues that focus on buying sewing machines.
For carabiners and ropes, go to http://www.cmcrescue.com. If you want to use ropes and carabiners from your local hardware store instead, I would recommend taking out a large life insurance policy and naming a local charity as the benefactor first.
Another home-builder site is at http://www.hotairship.com.
If you want to look up FAR's, go to the FAR Index.
Great instruments for your balloon can be had at http://www.flytec.com. Be sure to get one with a temperature sensor, such as the 3040 model.