Hello, I am new to this site, but I would like to give my 2 cents here if you'll have it.
Machine quilting with a domestic machine can be done with a bit of practice. I have the Babylock decorators choice which does have the speed control. (one of my favorite features) Whether you have a this or not you can still machine quilt.
As some of the ladies suggest, you need to make some practice sandwiches, about 14 to 16 inches square are good sizes. You need to be relaxed and have a good grip on the fabric. This can be done with quilters gloves, secretary fingers (you know the littler rubber tips)or even those disposable rubber gloves found in doctors offices work well and are pretty cheap.
As for how fast to go, I suggest start with a speed you normally stitch at and then try to gradually increase to about double. You must move the fabric at the same speed as the machine. (that is the tricky part and that is where practice will make all the difference.) So start slow, move fabric slow, then go a bit faster and faster until you reach a point that you are comfortable.
When working on these practice pieces think of it like doodling. just make loops and swirls or squiggles. Don't worry about crossing lines, or how good they are, this is the practice piece. You will know it is right when your stitches are even and look like normal stitches. If they are too large then you are moving the fabric to fast, and if they are too small then you are not moving it fast enough.
Moving at the wrong speed can break needles and can damage your bobin case. (I know this from personal experience) Because you are pushing and pulling the needle while it is still in the fabric. the machine does not like that. So if you feel better slow, just be sure you are moving fabric slow to avoid stress on the needle.
Making practice squares before any project is good advice. If you want to try a design like continuous hearts, try drawing what you want and tracing over the design 10 to 20 times with a pencil before you try it on fabric. This may sound silly, but it helps train the brain, and your hands to get the flow right.
Well ok, I think I gave more than 2 cents but the one common message I see on this subject is
practice
Take care and good luck!