The machine. It has been said that any machine that makes a good straight stitch can be used for free motion machine quilting. But I know quilters who will swear up and down that such and such machine is no good for free motion stitching. I think it comes down to knowing your machine and how much fiddling with it you need to do to get satisfactory results. Certainly the more harp-space/length of arm/throat/ or room to the right of the needle you have to work the better! But you can quilt smaller projects on a standard small sewing machine. I learned on a basic Kenmore machine, though I quickly wanted a bigger machine.
The surface: Above, you can see my main machine (Janome 6600P which has a 9 inch throat) is set flush with the counter top. This is especially nice as it gives a large flat, smooth area for the quilt to glide over. The wall behind (and off to the left of) the counter top keeps the quilt from falling off the edge or dragging on a corner. The best way to move your larger quilt sandwich is to 'puddle' it and keeping it on top of your surface is ideal. This can also be accomplished with a table set in a corner. I also have great lighting in this arrangement.
If you don't have your machine set into a table or counter top, there are extension tables available for many machines through their manufacturer or through a third party maker of extension tables. It is even possible to rig something up out of boxes or foam insulation board. The important point is to have a smooth area to glide the quilt over and as large as possible so the quilt doesn't get hung up on something and cause jerky movements while quilting. It is possible to FMQ without this surface, like on a regular sewing machine sitting on top of a table, but your left hand will risk falling off to the left side and your quilting will have to be very small movements. It is worth trying to get something set up to the the left of the machine.
The surface needs to be smooth and slick to make moving the quilt as easy as possible. I love my Supreme Sliders (Supreme Slider (original size) for my Janome 3160 and Queen Size for the larger Janome 6600) for how smooth it makes the area where my hands are when quilting, covering gaps between the machine and the table.
Grip: You need some extra grip when quilting and there are various ways to do this, but my tried and true way is with Machingers Gloves . Gloves can be a hassle sometimes, so I'll try something different from time to time, but I always come back to the Machingers, as seen below. I have fairly pudgy hands and I still like the fit of the small/medium gloves.
Feed dogs: Typically, the feed dogs need to be lowered for best results and the stitch length needs to be set to zero. When free motion quilting, the movement of your hands determine the stitch length, but setting the length to zero keeps the feed dogs from moving back and forth inside your machine, causing unnecessary wear. Some folks either can't lower the feed dogs or feel they get better results by leaving them up, so they set the stitch length to zero and cover the dogs with the supreme slider, index card, or special plate. The button or lever to lower the feed dogs is more easily accessible on some machines, others are very awkward to reach.
The foot: Next is the free motion foot which come in various styles. In the above photo are two basic common darning or FMQ feet styles above the ruler and below the ruler is my fabulous Janome convertible FMQ foot set. (Just to the right of it is the ruler toe that can be attached to it for ruler work like long armers do.) I love the convertible set and it is made in high and Low Shank versions so it will fit many other machines than just Janome. There is also a lower-priced and more basic FMQ foot like the convertible set with the adjustible height, but with only a fixed closed toe.
A basic darning foot can work of course and that's what I have for my smaller machine, below. When quilting, you want the foot to just barely push down on the top when the needle goes into the quilt sandwich, and rise above it when the needle is out. If it is set to low, it will cause drag on the movement of the quilt. Too high and you can cause needle deflection problems, skipped stitches, and risk breaking the needle. It is adjusted by changing the presser foot pressure on your machine or by adjusting the foot itself. On the convertible foot set, the spring can be tightened or loosened with a handy screw knob. On the basic darning foot, you can wrap a rubber band around the shaft above the spring to lift it higher.
The Needle: For the needle in your machine, a topstitching needle is best in my opinion (See edits below) and the 90/14 size works for most quilting thread. The top stitching needle has a nice long eye and a long, deep groove in the shaft to protect the thread as it moves through the top many times as each individual stitch is formed. It excels when using larger or specialty threads. I have used a size larger for my doodle stitching with heavier thread and a smaller for finer threads. Quilting, universal, and microtex needles have a place in your machine quilting toolbox as well. There is a fabulous article in the May/June issue of Machine Quilting Unlimited on all types of machine needles.
Edited to add: I no longer favor the top stitching needle more than other needles. It all depends on the combination of thread choice and thickness/density of your project. I've come to this conclusion after talking to my machine's dealer. He solved an issue I was having by explaining that one draw back to the top stitch needle is the larger eye, which can lead to sloppy stitch formation. If you are having thread shedding issues change the type of needle and see if that helps.
One thing to emphasize is that if you are having skipped stitches, increase the size of the needle.
The stitch plate: Edited to add: I forgot to mention the stitch plate! In the photo above you can see that the wide stitch plate is on this machine. Ideally, you want to put a straight stitch only stitch plate onto your machine as this helps with control of the top and backing, keeping the sandwich from tucking down into the hole with each stitch. It doesn't always happen, but it can really help to have that small hole for the needle to go into instead of a big slot.
Make sure you remember to switch back to a wide stitch plate before using anything other than a straight stitch! I use a large Post-It note over the stitch selection buttons when the straight stitch only plate is on the machine. I forgot to tell you about this because I don't always do this with my machine. The straight stitch only plate for my machine is still a wide oval so I don't always see a big difference, but it does add extra time to switch back to the wide plate. There are some newer, more expensive Janomes available which are much easier to switch out the plates or they go from wide to single hole with a touch of a button; I don't really want to change machines, but that ability would be handy!
Machine features: There are two handy features in a machine to be used for free motion quilting. One is a speed control slider (or other control) to adjust the top speed of your foot pedal.The other is a needle up/down function. That is the button with the two triangles on it on my machine. The needle down button makes the needle stop in the quilt sandwich when you stop stitching. This helps keep the quilt from shifting when you are moving your hands.
Bobbin case: A word about the bobbin case; Janome sells a special bobbin case for free motion quilting. I do not have it. I have found it unnecessary to fiddle with my machine's bobbin tension for quilting unless I am using a very fine thread in the bobbin while quilting with heavier thread on the top. I do have an extra bobbin case that I use when I need to fiddle with the bobbin tension so that I don't change the original bobbin case. But again, I rarely find it necessary to change the bobbin tension when quilting. (Edited to add: Vivian sent me a note to say she recently bought the free motion bobbin case for her Janome and has found it useful, especially with differing threads in the bobbin from the top.)
Extras: I use Little Genie Magic Bobbin Washers in my (drop in, top loading) bobbin case. I'm not entirely certain they're necessary, but they are easy enough to use and they are supposed to help the bobbin thread feed out more smoothly. They're cheap and seem to last forever.
The last thing for your free motion set up, and it's certainly not necessary, is a self-threading needle for burying threads (my post on it, also a video of mine), if you desire to bury them. I do. A spiral eye needle can work well too. Hopefully you can see the needle right in front of the yellow butterfly pin.
That's enough for this installment of How to Free Motion Quilt and should get you all set up. After you've gotten all set up, make some quilt sandwiches to practice on and check out these posts:
How To Free Motion Quilt; Basic Motion and Tension
How to Free Motion Quilt: The Designs
I hope you've found this extremely long post of use and let me know if I've missed anything or ask a question in the comments and I'll do my best to respond.