Catching cicadas was a popular activity for children when I was a childyoung in a small village.

"When I was a child" is a bit redundant since the phrase "when I was young" conveys the same meaning. The word "young" also sounds more natural in this context.

The first onemethod was to use a long hair from a horse’s tail to bind the cicadas.

"The first one" sounds a bit informal. "The first method" makes the sentence clearer. Adding "the" before "cicadas" makes the sentence more grammatically accurate.

Children first found a long and thin bamboo first, then attached the hair to the thin end of the bamboo after making ithe hair into a slipknot.

The phrase "found a long and thin bamboo first" sounds a bit awkward. "First" should come after the subject for better flow. "The hair" should be changed to "it" for clarity, referring back to the hair.

They held the bamboo, let the slipknot go around athe cicada’s neck, and pulled the bamboo to bind ithe cicada.

"A cicada’s" should be changed to "the cicada’s" because you are referring to a specific cicada being caught. "It" at the end replaces "the cicada" for more fluid and less repetitive writing.

The second method was to use gluten to stick the cicadas.

Again, change "the second" to "the second method" for clarity. "the cicadas" is needed here to make the sentence grammatically correct.

Children grabbed a little bit of wheat flour and made it into gluten;, then attached the gluten to the thin end of the bamboo, then used the gluten and used it to stick the cicadas’' wings.

Changing the semicolon to a comma and restructuring the sentence makes the sentence more fluid and less disjointed.

The third method was to use a small, empty plastic bag for laundry detergent to cover the cicadas.

Again, "the third" should be "the third method" for clarity. "Small empty" should be changed to "small, empty" because adjectives should be separated by a comma in this case.

Children found a piece of wire, threaded it athroundgh the opening of the bag, attached the bag to the thin end of the bamboo, and used ithe bag to cover the cicadas.

"Threaded it around the opening" is awkward; "threaded it through the opening" is the correct expression for this action. "Used the bag to cover cicadas" should be changed to "used it to cover the cicadas" for smoother reading.

Children first found a long and thin bamboo first, then attached the hair to the thin end of the bamboo after maktying the hair into a slipknot.

Your original sentence is okay, but I'd prefer it if "first" was moved forward. I think it sounds more natural that way.

The second was to use gluten to stick to cicadas.

Children grabbed a little bit of wheat flour and made it into gluten;, attached the glutenpplied it to the thin end of the bamboo, then used ithe gluten to stick to cicadas’ wings.

(1) attach: join or fasten (something) to something else. "attached" doesn't strike me as very natural in the context of gluten. Perhaps the word you're looking for is "applied".
(2) Incorrect use of the semicolon. It is used to link two independent clauses together, but "made it into gluten" and "applied it to" are not independent, because they are part of the same series of actions.
(3) I replaced "the gluten" with "it" to avoid excessive repetition of the phrase.
(4) Alternatively to "stick to cicadas' wings": "stick cicadas' wings together." The meaning is slightly different though, so it depends on what you want to imply.

The third was to use a small empty plastic bag for holding laundry detergent to cover cicadas.

It might not be clear what the plastic bag is used for. I'd suggest making it explicit.