A bodice lining has several purposes. It adds fabric weight to the bodice portion of a dress or top, which makes it sturdier and longer-wearing, for one thing. It finishes the inside of the bodice, since at least some of the seams will be encased between the two layers. In fabrics that wrinkle, the extra layer stiffens them up a bit and cuts down on a little ironing, I've found. I usually line the bodice of dresses I sew, for all these reasons and because I'm not a fan of facings. Facings tend to flop around and end up in the wrong places. Linings generally stay put.
A bodice lining can be made in the same fabric as the dress, because it's easy to just cut another set of bodice pattern pieces from the fabric you've already got spread out, or they can be cut of another fabric. If the fabric you're using for the garment you're making is heavy, or expensive, or hard to work with, or very thin, you might want to use a lining that compensates for those qualities. You can see in the photos below that I've used "self-fabric" (the same fabric as the bodice) for some of these bodices, and a different fabric for others.
The first step to lining a bodice is to sew the shoulder seams in the bodice itself, and then sew the shoulder seams in the lining.
Here, then, is a bodice ready for joining up with its lining:

To this particular neckline, I've added piping. If you're doing that, baste it along the neckline. If not, disregard the piping in the following photos, because the process is the same.

Here's the back, with the piping basted in place:

The bodice is right side out. Now turn the lining wrong side out and slip it over the bodice. Right sides of the bodice and lining are now facing each other. Match up the shoulder seams, center fronts, center backs, and front neckline shape. Pin like a madperson.
Now stitch the bodice to the lining at the neckline.

Okay, a few things here.
-If you've put in piping, you'll need to sew close to that, probably using a zipper foot or something similar. (I have used a pintuck foot to work with piping, with very good results.)
-If you're working with a slippery fabric, or you're at all concerned about the layers shifting while you sew, begin at the center front and sew to the center back, then come back and do the other half of the neckline.
-If you're using a button closure, you'll want to pivot at the back neckline edge and sew all the way down the back to the waistline, like this:

(I've added a strip of interfacing here, on both sides of center back, to help this quilting-weight cotton fabric take the stress of buttons and buttonholes.)
-If you're adding a zipper, however, you'll want to stop sewing the neckline at the center back, like this:

to allow you to put the zipper in.
Now you'll need to clip the neckline's seam allowance. Necklines with angles need to be clipped into the angles, not cutting through the seamline, thus:

And those with curves will need to be clipped like so:

Before turning right side out and pressing. Don't, please, put the iron down where you've clipped and hit the steam button. The fabric will collapse down into the little gap and look ugly. Turn the steam off, if you can, and just use the edge of the iron to press the neckline seamline only, not the seam allowance. Roll the lining slightly to the inside as you press, especially if it's a different color than the bodice.

If you're going to add sleeves, baste the lining to the bodice all the way around the armhole, on the seamline, to keep the layers from shifting while you do that:

Now those layers will be treated as one when you set in the sleeve.
If you'll be treating the bodice and lining as one layer at the waist seam, baste all along the waist seam now.
If you'll be using the lining to cover the waist seam, then leave the lining and bodice unbasted at the waist. After sewing the bodice to the skirt at the waist, you'll then turn up the seam allowance of the lining and handstitch it to the waist seam. The finished product will look like this:

Or you could use a slipstitch, instead of my whipstitch, for a less-obvious finish. I do like finishing the bulky waist seam in this way, but I find that it's tough to get the bodice and lining to end up exactly the same shape somehow. One or the other is always a hair tighter, leaving the looser layer to end up a little baggy looking. So I do this:

I find that careful pinning and smoothing, making sure the seams match and everything's in place, and then folding up my seam allowance and hand stitching it to the waist seam makes the end product look much more professional, and I get to keep my covered waist seam.
I do love a lined bodice. Don't you?
~E~