Take a tupperware container with a reasonably tight fitting lid, poke a couple holes in the top for gas exchange, a few small holes, nothing big like a loose fitting lid would give.
Depending on the food you're drying and it's water content, you'll need more or less dry ice. I start with about equal ratios and move up from there.. Honestly for most things you can probably start with double, but for flowers/herbs use about 1:1, somethings you need alot more.
Put dry ice on the bottom of the tupper, place item to dry on top of the dry ice.
Place in freezer, check progress 12 hours later, add more dry ice as needed.
Eventually you'll know how much dry ice you need to complete the process.
Also, if you have a freezer in bad shape it may cause issues.
The idea is to have the dry ice in an environment with a near 0 relative humidity. When something is enclosed with the dry ice in these conditions, water molecules migrate to the dry ice, causing the relative humidity of the co2 to increase and the moisture content of the item being dehydrated to decrease.
Now, the temps can cause issues with real watery stuff. I've only used this method 5 or 6 times with varying levels of success. I've heard some people use a cooler in some environments with different things also.
Also, I've had great luck using this with already partially dried items.
YMMV, obviously, this is a hack method.