I'd say just setting the blocks on top of the cloth would be sufficient. However, you can get staples to drive into the ground if you wish.

Good luck, welcome and enjoy your garden!

Here is a link that might be useful: Sinfonian's garden adventure

If your site is perfectly level, setting the blocks on top of the wire mesh will do just fine. But, chances are - most sites aren't perfectly level. Is yours? If not, I would build my block walls, then cut the mesh to fit perfectly on the inside. Then, you can take some 2 foot long pieces of small diameter rebar, and bend a small 90 degree angle on one end. After that's done, simply drive the rebar into the ground at several locations throughout the mesh, allowing the "L" to hook over the wire.

EG