Hodie magis quam heri laboro.

A quick breakdown:

• hodie = an adverb meaning today
• magis = a comparative adverb meaning more
• quam = than, used to introduce the second part of the comparison
• heri = an adverb meaning yesterday
• laboro = I work / I am working, first person singular present active indicative of laborare

So grammatically, this sentence is mostly adverbs + verb. There are no nouns here.

In Latin, the verb ending often already tells you who the subject is.

• laboro ends in -o
• that ending means I

So Latin usually does not need a separate word for I. The subject pronoun ego is normally left out unless you want emphasis.

For example:

• laboro = I work
• ego laboro = I work, with extra emphasis on I

Magis is an adverb, and here it modifies the verb laboro.

That means it tells you the degree of the action: not just I work, but I work more.

So the comparison is about how much or to what extent the speaker works today compared with yesterday.

Quam is the normal word used after a comparative expression to mean than.

So:

• magis ... quam ... = more ... than ...

In this sentence:

• magis quam heri laboro means I work more than yesterday

It connects the first side of the comparison, magis, with the second side, heri.

No. Heri is already a complete adverb meaning yesterday.

Latin often uses simple adverbs for time expressions:

• hodie = today
• heri = yesterday
• cras = tomorrow

So there is no need for a preposition. English also does something similar when we say today and yesterday without on.

Here they are just adverbs.

A beginner might wonder whether these are some kind of case forms, but in this sentence they function simply as time adverbs:

• hodie tells when the action happens now
• heri gives the point of comparison in time

So this sentence does not contain any noun cases at all.

Laboro is present tense: first person singular present active indicative.

Latin present tense can often be translated in more than one natural English way, depending on context:

• I work
• I am working
• sometimes even I do work

In this sentence, English usually prefers I work more today than yesterday, but I am working more today than yesterday could also fit in the right context.

Yes, Latin word order is flexible.

Because Latin marks a lot of grammar in word endings, the words can often move around for emphasis or style. The sentence could be rearranged in several ways, such as:

• Magis hodie quam heri laboro
• Laboro hodie magis quam heri

The original order is very natural. It starts with hodie, which gives the time frame right away, and puts the verb laboro at the end, which is also very common in Latin.

Still, even though the order can vary, magis quam heri works together as the comparison, so those words usually stay fairly close in sense.

Yes, you could, but it would sound more emphatic.

Since laboro already means I work, adding ego is not necessary unless you want to stress the subject:

• laboro = plain I work
• ego laboro = I work, perhaps contrasting with someone else

So if the point is simply the fact of working more today, Latin usually leaves ego out.

Both can relate to the idea of more, but magis is the more standard choice for comparing the degree of an action, adjective, or adverb.

Here the sentence is comparing how much the speaker works, so magis fits very well.

A simple rule for learners is:

• use magis for more in comparisons of degree
• think of plus more often as more in amount/quantity

So magis quam heri laboro is the idiomatic way to say this.

No object is needed.

Laborare often works as an intransitive verb, meaning to work or to labor. That means the action does not need a direct object.

So laboro by itself is a complete idea:

• laboro = I work

The key pattern is:

• time adverb + comparative adverb + quam + comparison word + verb

More specifically:

• hodie = the time of the main action
• magis quam heri = the comparison
• laboro = the main verb

A learner can remember this as a very common Latin comparison structure:

• magis ... quam ... = more ... than ...