Toto je naše společné dílo.

Toto means this and is a more explicit or slightly more formal/literary form than to in this kind of sentence.

So you may hear both:

• Toto je naše společné dílo.
• To je naše společné dílo.

In everyday spoken Czech, to is often more common. Toto can sound a bit more pointed, as if you are clearly indicating something right here.

Because naše has to agree with dílo.

The noun dílo is:

• neuter
• singular
• nominative case

So the possessive náš changes to the matching form:

• masculine singular: náš
• feminine singular: naše
• neuter singular: naše
• plural: naše / naši depending on gender and animacy

Here, since dílo is neuter singular, the correct form is naše.

For the same reason: adjectives must agree with the noun they describe.

Dílo is neuter singular nominative, so the adjective společný becomes společné.

Compare:

• společný projekt = a joint project (masculine)
• společná práce = a joint work/task (feminine)
• společné dílo = a joint work/creation (neuter)

Dílo is neuter.

One clue is the ending -o, which is very often a neuter noun ending in Czech. Not every noun follows a simple rule, but -o is a strong hint.

So:

• dílo = neuter singular
• therefore: naše společné dílo

It is in the nominative.

In a sentence with je (is), both sides can be in the nominative when you are identifying or equating something:

• Toto je dílo.
• To je můj dům.
• Tohle je naše škola.

So dílo stays in the basic dictionary form here.

Společné means something like:

• joint
• shared
• done together
• sometimes common in the sense of belonging to both/all of us

So naše společné dílo suggests something created together, not just something both people happen to own.

Because Czech does not use articles like English a/an/the.

So Czech simply says:

• Toto je naše společné dílo.

English has to choose something like:

• This is our joint work.
• This is our shared creation.
• This is the work we created together.

Czech leaves that article idea unspoken.

Yes, Czech word order is more flexible than English, but different orders change the emphasis.

The neutral order here is:

• Toto je naše společné dílo.

You could move words around in some contexts, but it would sound marked or emphasize something specific. For example:

• Naše společné dílo je toto.
  This sounds contrastive, like This is our joint work as opposed to something else.

For a learner, the original order is the best and most natural one to use.

A rough guide:

• Toto ≈ TO-to
• je ≈ ye
• naše ≈ NA-she
• společné ≈ spo-LECH-nay
• dílo ≈ DEE-lo

A few useful points:

• š sounds like sh
• č sounds like ch in church
• é and í are long vowels
• j sounds like English y

So je is not like English jee; it is more like ye.

Yes. Tohle is another common way to say this.

So these are all possible:

• Toto je naše společné dílo.
• Tohle je naše společné dílo.
• To je naše společné dílo.

Very roughly:

• toto = more explicit, sometimes a bit formal/bookish
• tohle = common spoken this
• to = very common and simple, often used in speech

Not exactly. Dílo often means a work, piece of work, creation, or work of art/literature rather than just everyday work in the sense of labor.

For example, Czech often uses:

• práce for work/labor/job
• dílo for a created work or result of creation

So in this sentence, dílo suggests a finished creation or result, not just the act of working.