The background needs to be one inch bigger on each side, so that actually means two inches larger (it took me a while to actually get this) So in my case I make a 4.5" inside hexagon and cut a 6.5" hexagon for the background.
Make sure to miter those corners carefully.
For joining hexagons together you can use a zigzag or a decorative stitch.
The advantage of this method is you can just continue to grow the quilt.
There is a lot more work and time up front, but when you are done putting the blocks together, they are done forever.
It does also take a lot of fabric. Three yards of fabric yielded about 90 6.5" hexagons for the background.
Please let me know if you have any questions or I made any errors.