The verb 返す (かえす) means "to return; to give back."

Quiz!

DUN DUN DUN...

What is the masu-stem of 返す?

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Hint: To get the masu-stem, you first need to know the masu-form.

What's masu-form, again, you ask? Well, it's basically the formal present or future tense of verbs.

Gigantic Hint: The masu-form of 返す is 返します (かえします).

So the masu-stem is...

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Bzzzz. Time's up, sucker.

The answer is: 返し (かえし).

If you don't know the rules for putting verbs into their masu-forms, thus figuring out their masu-stems, then... uh... I don't know. Go find a boring grammar book and use that. Or google "Japanese verb conjugations."

I would make charts with all of that stuff here, but it bores me to death.

Anyways...

JLPT N3: ～ようがない

Step #1: Take the masu-stem of a verb.
Step #2: Add ようがない.
Step #3: You can now say "there is no way to VERB."

#1: 返し (かえし）
#2: 返しようがない
#3: 返しようがない = "there is no way to give (something) back"

Let's look at that example in a sentence:

貸した本を返せと言われても、本など借りていないのだから、返しようがない。
かした　ほん　を　かえせ　と　いわれても、　ほん　など　かりていない　の　だから、　かえしようがない。
Even if he says to return his book, I haven't borrowed any book, so it's not like I can return one!
Literally: "lent + book + を + give back (command form) + と + even if was told, + book + など + have not borrowed + の + だ + because, + there is no way to return it."
Note: The nuance of など in this sentence is something like "and stuff." A more direct translation might be "and so forth."

Typically, this grammar construction will be used when the speaker wants to do something but has no way of doing it.

That's why we can often translate it as "there's no way to VERB."

One of my books says that it may help to remember that in this case the kanji for よう is 様, which we can think of as meaning "way."

I'm not a big fan of that pointer because this kanji has far too many uses. For one thing, at the end of someone's name it's 様 (さま), which is a super-honorific suffix. As よう, the kanji can also mean things like "appearance," "style," etc. Oh and when we repeat it twice we get 様々 (さまざま), meaning "various; varied; diverse."

Long story short, there are so many meanings for よう that I have no idea what it means anymore.

But, whatever. Let's get back to "there's no way to VERB."

I probably should have mentioned a while back that ～がない means "there is not." The verb ない means "to not be; to not exist." We can also use the masu-form, which in this case will be ありません.

For each of the following examples, first I'll give the VERB, then I'll give the sentence it appears in.

気を付ける
き　を　つける
to be careful; to watch out; to take care
Literally: "spirit + を + attach / apply / affix."

乗客にとって、飛行機事故は気を付けようがない。
じょうきゃく　にとって、　ひこうき　じこ　は　きをつけようがない。
For passengers, there is nothing they can do to avoid plane crashes.
Literally: "passenger + for (=from the perspective of), + plane + accident + は + there is no way to be careful about it."

失敗する
しっぱい　する
to fail; to mess up

米と水を入れてスイッチを押すだけなのですから、失敗のしようがありません。
こめ　と　みず　を　いれて　スイッチ　を　おす　だけ　なのですから、　しっぱい　の　しようがありません。
All you have to do is put in the rice and the water and switch it on, so there's no way to mess it up.
Literally: "rice + と + water + を + put in (and) + switch + を + press + only + なのです + because, + mistake + の + there is no way to do."

If you're wondering where in the world that の after 失敗 is coming from, then you are too inquisitive and should stop asking questions that are hard for me to answer.

I'll try, though...

Have you ever heard the word 仕方 (しかた)? It means, "a way; a method."

The most common way to see this word is in the phrase 仕方がない (しかたがない), meaning "it can't be helped," or "it's no use."

A shortened, more casual form of this phrase is しょうがない. It just now occurred to me that ～しようがない (notice the full-sized よ) may in fact be the full version of しょうがない (small ょ)... though しようがない (big よ) cannot be used in isolation.

Now, let's look at that with 失敗 (しっぱい // failure).

失敗の仕方（しっぱいのしかた）
失敗のしよう（しっぱいのしよう）
way of failing

Makes sense, I guess. (It actually makes very little sense to me. T_T).

Danger! I am running the risk of teaching you incorrect phrases. Keep in mind the following...

These are correct standalone sentences:
仕方がない。(It can't be helped.)
しょうがない。(It can't be helped.)

This is not a complete sentence:
しようがない。

Well, now that we're all sufficiently confused, let's move forward...

Our last example is a form of this grammar construction that is so common, it shows up in dictionaries on its own:

どうしようもない。
Nothing can be done about it. // It's hopeless. // There's nothing I can do.

Example:

彼女に謝りたいのだが、電話にも出てくれないのだからどうしようもない。
かのじょ　に　あやまりたい　のだが、　でんわ　に　も　でてくれない　のだから　どうしようもない。
I want to apologize to her, but she won't answer her phone, so there's nothing I can do.
Literally: "she + に + want to apologize + のだ + が (=but), phone + にも + won't answer (=go out [and] + won't give [me]) + のだ + because + there is nothing that can be done."

You may also be interested to know that when you're facing an impossible dilemma, you can say:

どうしよう...
What should I do...

Or you can ask your friend:

どうする？
What should we do? // What are we gonna do?

The most confusing part of all of this is that all by itself どう means "how." Go figure.