Servus clavos figit, et faber malleo tectum firmum facit.

Both servus and faber are in the nominative singular, which is the normal case for the subject of a clause.

• servus = nominative singular
• faber = nominative singular

A native English speaker often expects a masculine singular noun in Latin to end in -us, but some second-declension masculine nouns end in -er instead.
So faber is just a normal dictionary form: faber, fabri.

The ending -t shows third person singular present active indicative.

So:

• figit = he fastens / he drives in
• facit = he makes

That matches the singular subjects:

• servus figit
• faber facit

Latin often leaves he/she/it unstated, because the verb ending already tells you the person and number.

Because clavos is the direct object of figit, and it is plural.

Its dictionary form is clavus, -i = nail.
Here the sentence needs nails, so Latin uses the accusative plural:

• nominative singular: clavus
• accusative plural: clavos

So clavos figit means he is doing the action to the nails.

Figit comes from figo, figere. Its basic idea is fasten, fix, or drive in.

With clavos it naturally means something like:

• drives in nails
• fastens nails
• fixes nails into place

So it is not just a vague does something to nails; it has the more physical sense of fixing or driving them in.

Malleo is in the ablative singular of malleus, -i = hammer.

Latin often uses the ablative of means/instrument without a preposition to express with, by, or by means of something.

So:

• malleo = with a hammer

English usually needs a preposition, but Latin often does not.

Because tectum is the direct object of facit.

Its dictionary form is tectum, -i, a neuter noun meaning roof.
In this sentence it is accusative singular:

• nominative singular: tectum
• accusative singular: tectum

For neuter nouns, the nominative and accusative singular are often the same in form, so you have to use the sentence structure to tell its job. Here faber is the subject, so tectum is the object.

Because firmum agrees with tectum.

It is an adjective meaning firm or strong, and it matches tectum in:

• gender: neuter
• number: singular
• case: accusative

So:

• tectum = neuter singular accusative
• firmum = neuter singular accusative

This is a very common Latin pattern: facere + object + adjective = to make something [adjective].

So tectum firmum facit means he makes the roof firm/strong.

Not necessarily. Here facit means makes in the sense of renders or causes to be.

Because it is followed by:

• an object: tectum
• an adjective describing the result: firmum

So the idea is not mainly he constructs a roof from nothing, but rather he makes the roof strong.

This is a very common use of facere in Latin.

Latin word order is much more flexible than English word order because the case endings show what each word is doing.

So even though English needs a more fixed order, Latin can move words around without creating confusion:

• faber is still the subject
• malleo is still the instrument
• tectum is still the object
• firmum still goes with tectum
• facit is still the verb

The order here is perfectly natural Latin. Also, Latin very often puts the verb near the end of the clause.

Latin does not have articles like English the and a/an.

So a noun such as servus can mean:

• a slave
• the slave

and faber can mean:

• a craftsman
• the craftsman

You decide from context which English article is best.

Et simply means and.

Here it joins two clauses:

• Servus clavos figit
• et faber malleo tectum firmum facit

So it links two separate actions in the sentence.

Yes, it could come before. Latin adjectives can appear either before or after the noun they modify.

So both of these are possible in Latin:

• tectum firmum
• firmum tectum

The meaning would stay basically the same, because the agreement endings show that the adjective belongs with the noun. The chosen order is just one natural Latin arrangement.

A learner often wants to know how to look the words up. The main dictionary forms are:

• servus, servi = slave
• clavus, clavi = nail
• figo, figere = fasten, drive in
• faber, fabri = craftsman, artisan
• malleus, mallei = hammer
• tectum, tecti = roof
• firmus, -a, -um = firm, strong
• facio, facere = make, do
• et = and

That helps explain why the forms in the sentence sometimes look different from the dictionary form: Latin changes endings to show grammatical function.