The *easiest* way to put a backing layer on a quilt is to do the "inside-out" technique (also called the "quick turn" method)... it's commonly used to make quilts for charity, etc., since it's so quick and simple.

To do that, you'd lay your finished top (layer) on top of your backing fabric layer (right side to right side)... then lay your batting on top of them... they should all be the same size.
...pin all the way around using long pins (pins should be put in perpendicular to the edge)
....bring the whole thing to your sewing machine, and sew *almost* all the way around the quilt's outer edge, leaving a gap that's unsewn (say 8-12" wide... how wide a gap would depend on the size and the thickness of your quilt) --make sure to sew several stitches back and forth at each end of the stitching line to secure the thread there
....stick your arm into the gap, and grab a far corner of the unit from the inside... then pull it back through the gap slowly to turn the whole quilt inside out... it will now be the *correct* orientation --which is the top (facing out), the batting (hidden), and the back (facing back).
....turn under both sides of top/batting/backing in the gap area and pin them together ... then sew the two sides together along their top edges (blind stitch) to close the gap
Here's one photo of turning a quilt after the gap has been closed:

http://blankie.made4usa.com/StarIndex/QuickTurn/QuickTurn.html

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You can then do various things to the unit you've made to keep the layers from bunching or shifting too much in use. (Which you'd do would depend on the thickness of your fabrics, how much work you want to go to, and what you want it to look like when it's finished.)

The simplest thing would be to do nothing... (the outer portions of the quilt would look fairly puffy, and you might need a *little* ironing there to flatten out the seam--and also a bit more ironing after folding over the way it should be** which will also keep the backing fabric from showing on the front side too much).

The next simplest thing would be to do the step above**, then pin around the outer edges and sew a line all the way around the perimeter of the quilt 3/4" - 1 1/4"away from the edge (or as much as you want) to make the edge area of the quilt look more "finished."
This would be creating a "faux binding" -- the same color(s) as the quilt, rather than a binding fabric strip added separately.

You could then leave it just like that, or you'd have two other options to stabilize all the layers together:
...you could "tie" the quilt (easiest).
.. you could "quilt" the quilt (by machine or by hand)

If you tie the quilt, you'll simply stretch it out, then pin it in a number of places (often a grid, but could be any way you wanted). Then you'd "tie" through all the layers at each of those spots, using a piece of yarn (and a heavy duty needle with a long eye), or some kind of cording or even ribbon. Your needle would take a regular "stitch" through all the layers from the front side of the quilt, then come back out fairly close to the same area (may need pliers to help here) ... then you'd double-knot (or square knot, or surgeon's knot) the yarn/cording on the front side of the quilt, and trim the tails of the yarn/cording to the length you want (...I also always add a bit of Fray Check or even a dab of permanent white glue around the edges of the holes made by the yarn, to help strengthen those areas when the quilt is used).
You can also tie a quilt using "bar tacks" made on a sewing machine... that would be just sewing a number of wide stitches on top of each other in the same place.

If you machine quilt, you'd stabilize the quilt layers with pins or by hand sewing huge stitches all over it, then free-motion sew or sew in a particular pattern all over it. (look online for instructions).

If you hand quilt, you'd stabilize then put quilt any lines you wanted by hand in the same way. (look online for instructions)

HTH,

Diane B.