Uštedećemo novac.

Because Serbian usually drops subject pronouns when the verb already makes the subject clear.

In uštedećemo, the ending shows 1st person plural, so the meaning we is already built in.
You could add mi for emphasis, but it is not necessary:

• Uštedećemo novac. = We will save money.
• Mi ćemo uštedeti novac. = We will save money. (more emphasis on we)

This is a normal way of forming the Serbian future tense.

The verb is uštedeti and the future auxiliary is ćemo. When the auxiliary comes after the infinitive, Serbian often writes them together as one word:

• uštedećemo
• compare: ćemo uštedeti in a different word order

So uštedećemo is basically:

• uštede-
  • ćemo

This is very common in Serbian.

Because this future form is built from the infinitive stem, not from the present-tense stem.

The infinitive is uštedeti.
For the fused future form, you remove -ti and add the future auxiliary:

• uštedeti → uštede-
  • ćemo = uštedećemo

Even though some other forms of the verb use uštedi-:

• uštedim
• uštediš
• uštedi

the future written as one word still follows the infinitive pattern: uštedećemo.

It is future tense, 1st person plural.

So grammatically it means:

• future
• we

The auxiliary part -ćemo corresponds to we will.

Because novac is the direct object of the verb, so it is in the accusative case.

However, for many inanimate masculine nouns in Serbian, the accusative singular looks the same as the nominative singular.

So:

• nominative: novac
• accusative: novac

That is why the word does not visibly change here.

This is mainly a question of aspect.

• uštedeti is perfective
• štedeti is imperfective

So:

• uštedećemo novac suggests we will succeed in saving some money / we will end up with savings
• štedećemo novac suggests we will be saving money / we will economize

In other words, uštedećemo focuses more on the result, while štedećemo focuses more on the process or activity.

Yes, Serbian word order is fairly flexible, but not every order sounds equally natural.

Possible versions include:

• Uštedećemo novac.
• Novac ćemo uštedeti.
• Mi ćemo uštedeti novac.

A useful thing to remember is that ćemo is a clitic when written separately, and clitics usually do not stand at the very beginning of the sentence by themselves. So:

• Ćemo uštedeti novac. — not normal standard word order

Because Serbian has no articles like English a/an and the.

So novac can mean:

• money
• the money
• sometimes some money

The exact meaning depends on context.

A rough English-friendly guide is:

oo-shteh-DEH-cheh-mo NO-vats

A few important letters:

• š = sh as in ship
• ć = a soft sound somewhat like a very мягкий ch/t sound; English has no exact match
• c = ts as in cats

So novac sounds roughly like NO-vats.