Con il metro misuro il tavolo e segno ottanta centimetri sul foglio.

Here metro does not mean the unit meter. In this sentence it means a measuring tool, such as a tape measure, ruler, or meter stick, depending on context.

So con il metro means with the measuring tape / ruler / meter stick.

Also, con means with, and il is the.

Italian does have the contraction col = con il, and it is correct. But in modern standard Italian, people very often prefer the full form con il.

So both are possible:

• Con il metro misuro il tavolo
• Col metro misuro il tavolo

The version with con il sounds very normal and neutral.

Both verbs are in the present indicative, first person singular:

• misuro = I measure
• segno = I mark / I write down

They come from:

• misurare = to measure
• segnare = to mark, note, write down

The -o ending is the usual ending for I with many present-tense verbs in Italian.

Italian usually drops the subject pronoun when it is clear from the verb ending.

So:

• misuro already means I measure
• segno already means I mark / I note

You could say Io misuro il tavolo..., but io is normally unnecessary unless you want emphasis or contrast.

Italian uses definite articles very regularly, often more than English learners expect.

In this sentence:

• il tavolo = the table
• il foglio = the sheet of paper / the page

The article sounds natural because the speaker is referring to specific objects in the situation. Italian generally prefers the article here.

It can mean several related things depending on context. Here, segno ottanta centimetri sul foglio most naturally means something like:

• I write down 80 centimeters on the paper
• I mark 80 centimeters on the sheet

So segno is being used in the sense of marking/noting information.

Because here ottanta centimetri is the quantity being written or marked.

• ottanta = eighty
• centimetri = centimeters

Italian often uses measurements directly without di in this kind of structure:

• segno ottanta centimetri
• misuro due metri
• scrivo dieci numeri

You would use di in other patterns, but not here.

Sul is the combination of:

• su = on
• il = the

So:

• su + il = sul

That gives sul foglio = on the sheet of paper.

This is one of the common Italian preposition + article combinations:

• nel = in the
• del = of the / some
• al = to the
• sul = on the

Yes. Italian word order is flexible, although some versions sound more neutral than others.

The original sentence is perfectly natural:

• Con il metro misuro il tavolo e segno ottanta centimetri sul foglio.

You could also say:

• Misuro il tavolo con il metro e segno ottanta centimetri sul foglio.

This still sounds natural. The original version puts a little more focus on the tool con il metro at the beginning.

Because the speaker is describing two actions done by the same person:

1. misuro il tavolo = I measure the table
2. segno ottanta centimetri sul foglio = I write down / mark 80 centimeters on the paper

The conjunction e simply means and.

This kind of structure is very common in Italian: one subject, two coordinated verbs.

Usually foglio means sheet or sheet of paper. In many contexts, English might translate it as:

• sheet of paper
• page
• paper

So sul foglio literally means on the sheet, but a natural English translation may vary depending on context.

Grammatically, the sentence says the speaker measures the table and then marks eighty centimeters on the paper. In normal context, that strongly suggests the measurement obtained is 80 cm.

So yes, the natural interpretation is that the table measures 80 centimeters in whatever dimension is being measured, and that figure is then written down or marked.