Hammocks can be made with clips attached or only tabs for detachable clips. Metal clips can chip the enamel inside a washer or dryer. I find I need several, one is always in the wash.
For these projects I used
Polyester fleece stadium blankets from the thrift store for $2.00 each
Polypropylene webbing from a belt strap cut into 4" pieces.
and 4 swivel clips from an old purse (they don't HAVE to match)
cheap shower curtain hooks
Step 1: Make a Template or Paper Pattern
Or you draw something freehand.
Or cut a template from cardboard, this is best for rectangular ones.
Keep reusing the cardboard template to trace new ones.
For this particular design I made half the pattern, so that I can cut the material folded.
These are both 15 inches long by 13 inches wide, though they can be made wider or even smaller to fit smaller cages. I find with this size i can actually get TWO into one cage on different levels.
If you are making the 'sling' style, be sure to make the corners taper to no less than 4 inches wide to allow for webbing AND the turn.
Step 2: Cut Out Material
Trace and cut out TWO sides.
leaving 1/2 to 3/4 inches for the seam allowance.
If the top and bottom don't match perfectly, they can be trimmed AFTER you sew,
but it won't matter because it will be inside the hammock.
Step 3: Sew Around Edge While Attaching Tabs
insert the webbing tabs with or without swivel clips into the corners pointed inwards.
You are sewing around them and through the two layers of webbing.
Take 2 or 3 passes over the nylon webbing.
STOP sewing when you get within 4 inches of where you started.
You need this gap to turn it inside out.
Cats and small animals are not particular about fashion.
if the sides don't match perfectly don't fret.
The goal is to create something that will survive use and washing machine cycles.
Step 4: Turn the Hammock Inside Out
Pull the tabs and clips through this gap in the seam edge.
then finish by hand sewing the seam closed.
Use an invisible seam stitch if you can, otherwise just a secure overhand will do.
Step 5: Attach Clips
you can use simple shower curtain hooks.
Which should do nicely and can be removed for washing.