Ria asked, "I thought you put the fabric in a hoop while you stitch. Do you re-hoop it every time you work on it? Does it stretch the fabric if you leave it on a hoop?"
The answer to the first part is, "It depends."
You see some people like to work "in hand". That means that you don't use a hoop, or other stretching devise (and we'll come back to this later), you hold it in your hand and as you work on it you may need to roll or bunch it up to stitch depending on how large the piece is. This technique is very handy because you can carry your piece with you without it taking up a ton of room. I like to work in hand, and do most of my stitching that way. However there are times when that isn't the best choice.
The next option is a traditional hoop.
Next comes Q-snap frames. Made from PVC these frames come in a variety of sizes from 6"x6" to 17"x17". I remember the first time I saw Q-snaps. I loved them. They are light weight yet sturdy, don't snag your linen and can be rearranged to make all different sizes since they are modular pieces that snap together. I personally own some of every size. They do keep your fabric fairly taunt. Most people use a cotton fabric between the c-shaped clamps and the fabric they are working on to protect their stitches, especially if they are having to use a smaller sized q-snap than their design. Some just like how adding the extra fabric helps keep the fabric stretched.
Then there are frames. I actually have a couple of different types. The most common are scroll frames.
I have some scrolls that you don't have to sew the fabric on. Some have a groove in the scroll (dowel part) that a "thing" fits in that holds the fabric. I don't have a picture of this set, nor do I remember who the maker is. The "thing" that fits in the groove and holds the fabric are two very thin dowels that are held together. I haven't used this type in awhile, but may pull it out for one of my other pieces. The other type I have has just a plain dowel that you then use a Velco strip attached to the dowel and your fabric to hold the fabric on the dowel. I've never actually used these. I have the dowels and the Velco made for them. You do have to leave yourself an extra margin at the top and bottom because when you remove the Velcro from your fabric you probably have to cut it off.
Finally I have one other type of frame. Stitch Away mounts are handmade and come from Canada. I love it for smaller pieces. I own the smallest size and have had it for years. Learning to mount your fabric in the frame is different and takes some getting used to, but the results are great. Plus it's a piece that will be around for years.
Using a frame is nice, but you almost have to have a stand to put them in to be able to stitch without getting tired. I've owned a K's Creation Baby-z lap stand for a number of years and I like it because my Stitch Away mount, q-snaps and my scroll frames will all fit in the clamp.
I hope I've managed to answer the questions Ria had without muddying the water even more. Everyone has their favorite way of holding the fabric to put stitches on, no way is more correct than the other. The good news is there is a way that works for each person and for some of us it just depends on the project. Now, when can I teach you to stitch Ria???