After several months your Luffa plants will have grown into Monster vines! Which simply means you need quite a bit of space to grow them since the vines take off. I grew ours up on the chicken wire along a stone wall and even then they continued to grow into the surrounding trees.
Once the growing season has ended and the Luffa vines have started to die off, the Luffa itself will be green and heavy. Several months are needed once picked for the Luffa to dry out (several stages shown above).
Peeling off the dry outer skin reveals the Luffa inside which is also brittle and contains many seeds. You can cut the dried Luffa into smaller pieces or use as is. Make sure to save seeds to grow more next gardening season!