Here's my quick & dirty way to do a lined bag. I hope this makes sense. =)
EXTREMELY PICTURE HEAVY!
1. Cut two pieces of fabric, twice as long as it is tall. These are 5 x 10". Also grab a zipper that is longer than the short side of the fabric. I'm using a plain polyester 7" zipper.
2. Line up the short edges of the fabric with the zipper sandwiched in between. Whichever fabric you want for the exterior of the bag should be on the TOP side of the zipper. Sew these 3 together, as close as you can get to the zipper teeth, and as straight as you can.
3. Line up the other edges of the fabric with the other side of the zipper. Sew.
4. Pull the two tubes of fabric that you've just created, so that the zipper is as centered as you can get it. Make sure you pull the fabric rather taut so that you don't get any pinched or wrinkled bits. Sew across the bottom.
5. UNZIP THE ZIPPER. (you'll kick yourself later if you forget!). Pull the two layers of fabric in the other direction, centering the zipper between the two sides. If you want to insert a handle or strap of some sort, this is the time to do it. I usually put a bit of grosgrain ribbon or similar just in front of the zipper between the layers of the outside fabric. I'm using enough for a wrist strap, but you can use shorter, or nothing at all if you'd like
6. Sew this top seam, over the zipper, stopping about 1" or so from the end of the liner fabric. Trim off the excess bits of zipper from the top & bottom seams of your bag.
7. Turn the bag right-side-out by pulling it through the gap you just left in the lining. If you forgot to unzip earlier, you can cry now.
8. Push out the corners of the bag. Pull out the lining. You can now either topstitch the hole in the lining (which I do because it's inside & inconspicuous, and I'm lazy), or if you want a nicer finish, you can hand sew a slip or whip stitch. Push the liner back in.
Ta da! Once you get the hang of this, you can do them really quickly. Start to finish is probably less than 15 minutes!
If you want to be really fancy, you can put a bit of rick rack, cording, ribbon, lace, etc. in both the bottom & top seam for a fancier finish.