Мы как-то нашли способ.

In Мы как-то нашли способ, как-то most often means somehow or in some way.

So the idea is: We somehow found a way / We managed to find a way.

A useful warning: как-то can also mean once, one day, or at some point in other contexts. Its exact meaning depends on the sentence. Here, if the intended meaning is about managing to solve a problem, somehow is the most natural reading.

Because the subject is мы = we.

Russian past tense agrees with the subject in:

• gender in the singular
• number in the plural

So:

• я нашёл / я нашла = I found
• он нашёл = he found
• она нашла = she found
• мы нашли = we found

Since мы is plural, the verb must be plural too: нашли.

Because способ is the direct object of нашли.

The verb найти takes a direct object in the accusative case. For an inanimate masculine singular noun like способ, the accusative form is the same as the nominative:

• nominative: способ
• accusative: способ

So:

• Мы нашли способ = We found a way

If the noun were animate, the accusative would often look different.

The dictionary form is найти, which means to find.

Нашли is the past plural form of найти.

This verb is perfective, so it presents the action as completed:

• находить = to be finding / to find regularly / imperfective
• найти = to find, to succeed in finding / perfective

So Мы как-то нашли способ suggests a completed result: we did find a way.

Because the sentence focuses on the result: a way was found.

Compare:

• Мы находили способ would sound like we were finding a way or we used to find a way, depending on context
• Мы нашли способ means we found a way — the action reached its endpoint

Russian aspect is very important. Here, the speaker is not describing an ongoing process but a successful outcome.

Russian has no articles like a or the.

So способ by itself can mean:

• a way
• the way

You understand which one is meant from context.

In many cases, English would naturally translate this as a way:

• Мы как-то нашли способ = We somehow found a way

But in another context, the way could also be possible.

No, Russian word order is relatively flexible.

Мы как-то нашли способ is natural and neutral. But other orders are also possible, with different emphasis:

• Мы как-то нашли способ = neutral
• Как-то мы нашли способ = slightly more focus on somehow / one time
• Способ мы как-то нашли = stronger focus on способ

The meaning stays similar, but the emphasis changes.

Because как-то is a fixed form in Russian orthography.

Many Russian particles and indefinite-type forms are written with hyphens, and -то is one of them. Compare:

• кто-то = someone
• что-то = something
• где-то = somewhere
• как-то = somehow / somehow or other / once, depending on context

So the hyphen is just the standard spelling.

The main stresses are:

• мы
• ка́к-то
• нашли́
• спосо́б

So roughly: Мы ка́к-то нашли́ спосо́б.

A rough English-style approximation would be: mɨ KAK-ta nahsh-LEE spa-SOP

But it is best to learn it from native audio if possible, especially for:

• ы in мы
• the soft/hard consonant patterns
• the final consonant sound in способ

Yes, in some contexts как-то can mean something like once, one time, or at some point.

So depending on context, Мы как-то нашли способ could be understood as:

• We somehow found a way
• We once found a way

But if the sentence is about solving a problem, English usually prefers somehow. If it is telling a story about a past occasion, once may fit better.

Not exactly.

• способ = method, way, means
• путь = path, route, way
• возможность = possibility, opportunity

In найти способ, Russian usually means to find a method / a way to do something.

So способ is the best choice when you mean a solution or method, not a physical path and not just a possibility.