If you hand quilt and use a hoop, where do you start on a large quilt? in the middle and work out?, if so how do you keep the backing from buckling? or do you start on one side of the quilt and work to the other side? I have tried the hoop in the middle of the quilt and work out and baste the quilt with lots of safety pin, but my backing always has buckling somewhere.

I start in the middle.

The backing, batting, and top are layered and smoothed and basted together with a LOT of basting before being quilted. That really close, really smooth, real close basting is what keeps the final quilt smooth.

I dont like to use safety pins on big hand-quilting projects. I find that I put little poofs in the quilt sandwich when I use safety pins. I like good old fashioned basting stitches, and lots and lots of them. Basting is definitely not the most fun of making a quilt, but it's so important to the final product.

I lay out the backing fabric on the floor since that is the largest unoccupied place in my house, then I lay the batting on top, then next the quilt top. How can I make sure everything stays smooth while I baste it?

I've never liked using safety pins and prefer the slower hand basting same as Stitchinjoy.

in the middle and work my way around the quilt out.

I have made some sand bags to help hold it while I based

I start in the middle and work outwards. Just make sure the backing is smooth in the hoop before you quilt. When you move the hoop, again, make sure backing is smooth.
I baste on the floor and don't baste heavily. Usually 8 lengths of thread, radiating out from center.

How large are your basting stitches? I'm hand quilting my first quilt, having used safety pins, and there is lots of buckling on the back. For my next one, I'd like to try basting instead.

I use a hoop and start in the middle. I've hand quilted up to king sized quilts this way. It makes it easier to find where I've been working when I have to put it down.

For basting, I use my (folding) craft/cutting table. I center the backing and then use large binder clips on the edges to make sure it's smooth. Follow the same process for the batting and the top. When I have all the layers smooth, taut and clipped, I usually pin baste. If it's a really large (king) quilt sometimes I'll do thread basting simply because it makes the quilt that much lighter during the quilting process. Again, if it's a large quilt, I then reposition the sandwhich, sometimes mulitiple times, until I can get all the way out to all four edges. It can be tedious but it's far easier on my back/knees than doing it on the floor. Plus I don't have have that much open floor space.

I'm lazy....I use spray baste. Just finished one and it turned out great:)