There are at least a couple of other instructables for similar projects already, including this one, showing a similar crocheted tote, and this one, showing a knitted plastic handbag.

I use this as a motivation to never forget my reusable bags. Every time I forget them and end up bringing a plastic bag home from the store, I have to save it and eventually crochet it into a reusable bag. This has worked on me. I am getting really tired of crocheting plastic.

My stupidity and lack of discipline has paid off, though, in that I think I've nailed down the elements that make up a good, sturdy plastic bag bag. The flat, structured bottom lets you set your bags on the counter for easy packing and unpacking, and the attached handles are strong enough even when the bag is loaded down.

I am way too stupid and lazy to count stitches and come up with an actual stitch-by-stitch pattern, so you will have to eyeball things a little as you go along to get it the size and shape you like.

What you'll need:
Scissors
A whole lot of plastic shopping bags
Crochet hook, size N

Step 1: Make Plastic Bags Into Yarn

Note: I make yarn as I go along, so I only cut up one bag at a time. I find this is a little easier for me, as I don't have to keep track of a whole bunch of yarn at once, and it's slightly less tedious when you switch between cutting yarn and crocheting.

First, flatten your plastic bag as neatly as you can.

Keeping the bottom seam as flat, fold the bag vertically until it's maybe an inch wide, as shown in the second photo.

Snip off the bottom seam.

Cut the bag into strips anywhere from about .5 to 1 inch wide. This doesn't have to be perfect, and it doesnt' have to be consistent, so as long as the strips are thick enough to stay intact, and thin enough to work with, as in the third photo here.

Unfold the loops and connect them by using a girth hitch, described here. Pull the previous loop taut before attaching the next, so the loops are evenly spaced.

Step 2: Make the Bottom of the Bag

The bottom of the bag is a simple rectangle shape, for stability.

In this case,I've crocheted about 30 rows of 12 single stitches to form the bottom. You can vary the size, of course. I've found that a size N crochet hook is ideal for this.

Note that this made a humungous bag, and the bottoms always seem deceptively small to me.

If you want a more traditionally sized grocery bag, you'll want to make it more like 10 stitches across, maybe 20-24 rows.

Step 3: Finish the Body of the Bag

Once you've completed the bottom of the bag, you'll crochet in the round to complete the body. On the first body row, crochet two single stitches into each corner stitch, and crochet the rest normally.

Continue crocheting in the round, using single stitches, until the body is about the size you want.

Step 4: Add Handles

Note: If you prefer, you can count stitches to place the handles, but I've found that it's hard to accurately pinpoint the edge of the bag, and I get better results just eyeballing the bag and starting the handles where it looks right. Also note again that I am lazy and not particularly fussy.

Once the body of the bag is complete, you'll add the handles. Integrated handles work best for grocery bags, because they're more secure and less likely to unravel when you're carrying heavy loads.

To start the handles, flatten the bag, then measure equal distances from each edge to indicate where to start the handles. Place four markers at the positions where the handles begin. The handles will work outward, so you may want to make the openings slightly smaller than you picture the finished product. See the second photo for an illustration.

Continue crocheting the next round as usual, but when you reach the first marker, crochet a chain stitch, slightly longer than the gap between the first and second marker. See the third photo for this.

Attach the chain to the second marker, then continue crocheting until you reach the next marker, then chain stitch as with the previous, and attach again at the final marker. Do not make the handles too long, as they're pretty stretchy.

Crochet two to three more rounds, until the bag handles are the desired thickness, making sure you have the same number of rows in each handle.

Once the handles are complete, continue crocheting to the edge of the bag, then finish off, and you're done.

Now keep making these until you run out of disposable bags.

Step 5: Astonish Passersby With Feats of Strength

To demonstrate the capacity and stretchiness of these bags, here is one I've been using for over a year, filled to the bag's volume capacity with cans and jars.

The bag does stretch to accommodate what you put in it; and the handle stretches as well.

The final picture is the bag after I emptied it again. As you can see, the handle has stretched over time, which is why it's important not to make the handle too long in the first place. The handle is still very sturdy, though, and the body of the bag has no permanent stretching or breakage.