There are lots of different ways to construct a bag, one piece or several pieces, it all depends on how you want the bag to look when you are done. Sometimes, either for aesthetics or for functionality, you need a completely separate bottom on a bag. Sewing that rectangle on can be a swear worthy proposition without one simple technique.
Stat with five pieces, two sides, front, back, and bottom. The bottom on this bag is a long rectangle, but this technique would work with any shape including ovals and circles.
Match a side to the front and pin. When sewing, do not start at the edge of the fabric. Start sewing one seam allowance from the edge. I tend to sew my bags with 5/8" seam allowances because I learned to sew on clothing and any other seam allowance just feels weird. It can be hard to guess where 5/8" falls from the top edge of the fabric so I use a pivot technique to find it. In the following pictures, side B is the bottom edge and side A is the side edge.
I place the fabric in the machine so the needle is 5/8" from the edge of side B using my seam guide on the machine itself. I guess the distance to the edge of side A hoping I'm close to 5/8". Then with the needle down and without sewing, I pivot the fabric like so:
Side A is the side I intended to sew. If the edge of side A is not lined up with the seam guide on the machine, I back the needle out and carefully adjust to maintain the 5/8" distance from side B. Then I sew the seam, making sure I reinforce my stitching at the beginning of the seam. For me, this means reverse stitching back to the beginning of the seam and then sewing forward.
Your seam should look like this:
notice how there is that 5/8" that isn't sewn at the end of the seam there? Now you sew the other three sides leaving that 5/8" gap every time.
Then you are ready to pin on the bottom piece. This is where all that careful stitching really makes the difference. When you go to pin the bottom in, the corners sides will match up with no wrestling because the corners of the fabric can separate allowing the purse sides to turn at 90 degrees to each other.
Like this. See how I can match up the long edge and the short edge just folds neatly out of the way? When you sew the bottom seam, start and finish the width of the seam allowance from the edges again. Notice how in the next photo the stitching is rectangular. It never runs to an edge. Like this:
Now you just trim the seam allowance and flip it inside out. Sew the lining exactly the same way, but leave a gap in the stitching on one long edge to turn the bag through. When you are done your bag will have a structured defined shape. Like this:
And that's it. Simple, huh?