Here is a quick tutorial for making a lined tote bag. I have found that I can get nice results with a minimal amount of fuss using this method, it avoids all hand stitching and gives a nice finished look. I used quilting cotton for lining and outer fabric and fused iron on interfacing (medium or heavy weight) to all pieces which gives you a very structured tote that will stand up on its own. If you want something less stiff you could use interfacing on the outside only or not at all. Of course you could also use a heavier weight fabric in lieu of interfacing.
This bag was for my daughter and ended up about 8" wide by 10" tall and 3.5" deep.
Cut two pieces 12.5" x 12.5" of both outer and lining and two pieces 2" x 15" of each fabric for the straps. Cut the same size for interfacing for all pieces if you like. (1/2 yard is plenty for each fabric and you need 50" of interfacing that is 20" wide)
Fold the long edges of the strap pieces towards the middle. Put one outer fabric piece with one lining fabric piece and topstitch along the edges. Put the two lining pieces right sides together and sew up the sides, do the same for the outer fabric.
Turn outer fabric tube right side out, center and pin down the straps on either side.
Put the outer fabric tube with straps inside the lining tube so that right sides are together.
Sew around the top, turn and topstitch.
Make sure the bag is inside out and sew all layers together at the bottom. I like to use a 1/2" seam then trim to 1/4" and zigzag over the edge. If you have a serger I am sure it would be much easier to just sew up the bottom with that.
In the corners on both sides of the bottom mark out a 1.75" square from the folded edge and the seam. Pinch the corners so the lines line up and sew along the line.
Turn it right side out and you are done!