There are a lot of patterns and instructions for recycled plastic bag crochet out there, I'm just adding to the fun with this post and pattern.
This is a bag that I assisted my friend C. in making: a market bag with long straps, made of grocery bags (in white and brown) and target bags (the red speckles).
There are two reasons to crochet with plastic bags that currently apply to me: (1) because a crafter is on a yarn-purchase moratorium because said crafter's HVAC needs to be replaced, and (2) because a crafter wishes to be eco-friendly in a really flipping fun way.
What you need for plastic bag crochet
1) plastic bags - way more than you think
2) crochet hook - larger the better (within reason)
3) scissors - for cutting plastic bags
Crocheting with plastic bag yarn is a two-step process. First, you have to make the yarn, then you have to crochet it into a project of your choice. Projects can be bags (a postmodern reconfiguration of a highly wasteful object into one that we dub "eco-friendly"), bath mats, doggie beds, or anything else.
MAKE THE YARN
The yarn-making process involves cutting the bags into long loops of plastic, then threading the loops together to make a two-ply plastic yarn.
Get those bags and a pair of scissors. Lay a bag as flat as possible, then fold the bags in half length-wise twice or three times, until you can cut across the width with one snip of your scissors. First cut across the top to remove the handles. Then, cut across the bottom to remove the base. You now have a plastic tube which you will cut into loops.
A note about gauge
Depending on the size crochet needle you have, and your desired gauge, you can make this yarn thicker or thinner.
Another factor is the heft of the bags you are recycling. Some grocery store bags are much thinning than bags from department stores.
Here's a very arbitrary gauge chart, with suggested needles. The inch measurement refers to the width you will cut your loops:
.5"/thick bag or 1"/thin: Light weight. Size K (6-6.50)
1"/thick or 1.5-2"/thin: Medium weight. Size P hook. (10-11.5)
2"/thick or 2.5-3"/thin: Heavy weight. Size Q hook. (15-16)
When pairing yarn to your hooks, remember the proper pairing depends on (1) your personal crochet tension, and (2) how tight you want the work to be. I would suggest that you work this material tightly, though, to make a stronger fabric.
To attach the loops to make yarn
I know this sounds confusing, but it's a lot easier when you have the yarn in front of you to work with.
Lay one loop on the ground, then lay the second loop on top of it, overlapping slightly. Reach through the top loop and grab the edge of the bottom loop, pulling it through, and then thread this end over the top loop and through itself, i.e., through the bottom loop. Pull tightly, and the loop-over connects the two loops. Continue attaching the loops like this until you have a large ball. (And I mean large--like 1 foot in diameter.)
CROCHET THE BAG
I've prepared a simple bag pattern recipe. This is a tote with handles, not straps like the bag in the picture above.
The pattern presumes that you know how to single crochet flat and in the round.
Work the bottom of the bag
Chain (ch) about 16 inches. This length will be the width of your bag, so chain as many as you want depending on the size bag you would like to make.
Crochet flat with single crochet (sc) for 4-5 inches. This is the depth of your bag. Again, make it as large as you would like.
You will work the sides of the bag in sc. You will now work in the round, around the four sides of the rectangle you just made. As you work in the round, the bag will grow taller. Work for as long as you would like, creating the height of a bag you will want to use--18"-20" is what I recommend.
Work bag handles
First, you need to decide how wide you would like the handles to be.
Second, you need to figure out how to center that width on the width of your bag's long sides.
When you work the handles, you will sc as normal until the start of the handle, then ch as many sts as there are sts for the handle width, then reconnect and sc to the other handle location, repeat handle chain sts, and work to end of round.
The next round you will work in sc including across the chain.
Work in sc until the handle height measures 2-4 inches. Any less than 2 inches may sacrifice handle strength. Wider than 4 inches makes the handles difficult to grab.
You are finished! Tie off, weave in ends using your crochet hook.
Here's a ridiculous schematic I drew. I should stick to CAD software.