Đây là tiền tiết kiệm của tôi.

Đây means this or here, depending on context. In Đây là tiền tiết kiệm của tôi, it works like this in This is my savings.

A useful pattern is:

• Đây là ... = This is ...
• Kia là ... = That is ...

So đây points to something close to the speaker, either physically or in the conversation.

Là is the linking word used to connect two nouns or noun phrases, similar to is / am / are in sentences like This is my savings.

So the structure is:

• Đây = this
• là = is
• tiền tiết kiệm của tôi = my savings

Together:

• Đây là tiền tiết kiệm của tôi. = This is my savings.

In casual Vietnamese, là is sometimes omitted in some contexts, but in a basic identification sentence like this, keeping là is natural and clear.

Tiền means money.
Tiết kiệm means to save or saving/savings, depending on context.

So tiền tiết kiệm literally means something like saved money or savings money, but in natural English we would usually just say savings or saved money.

You can think of it as:

• tiền = money
• tiết kiệm = saving / saved

So tiền tiết kiệm = savings / money I have saved

Vietnamese possession usually comes after the thing being possessed.

So instead of saying my savings, Vietnamese says:

• tiền tiết kiệm của tôi
• literally: savings of me

This is a very common pattern:

• nhà của tôi = my house
• sách của tôi = my book
• xe của tôi = my car

English puts the possessor first (my book), but Vietnamese often puts it after the noun (book of me).

In standard Vietnamese, no, that would sound wrong here.

For regular possession, của is normally needed:

• tiền tiết kiệm của tôi = correct

Vietnamese can omit của with some very common personal relationships or fixed expressions, such as:

• mẹ tôi = my mother
• anh ấy = his older brother / he

But with things like money, book, car, etc., you normally keep của:

• sách của tôi
• xe của tôi
• tiền tiết kiệm của tôi

Yes. Tôi is a standard, neutral, polite way to say I / me.

In của tôi, it means my.

Vietnamese pronouns change depending on age, relationship, and situation, so in real life a speaker might also say:

• của em = my, if the speaker is younger/lower-status in the conversation
• của anh = my, if the speaker is an older male relative to the listener
• của chị = my, if the speaker is an older female relative to the listener
• của mình = my/our/one’s, depending on context

But tôi is a very safe pronoun for learners.

Not in the same way English does. Vietnamese does not use articles like a/an/the as a normal required part of nouns.

So:

• tiền tiết kiệm của tôi can mean my savings or the savings that are mine, depending on context.

Vietnamese relies more on context than English for this kind of meaning.

It is natural, especially if you are pointing something out or explaining what some money is.

For example:

• someone asks Whose money is this?
• you say Đây là tiền tiết kiệm của tôi.

Depending on context, speakers might also say:

• Đây là số tiền tôi tiết kiệm được. = This is the money I managed to save.
• Đây là khoản tiết kiệm của tôi. = This is my savings / my savings fund.

Your original sentence is correct and natural; these are just alternative ways to express a similar idea.

It can do both.

Most basically, đây points to something near the speaker:

• a stack of cash in your hand
• a bankbook
• a note on a screen
• an amount being discussed

So Đây là tiền tiết kiệm của tôi could mean:

• This cash here is my savings
• This amount is my savings
• This is the money I have saved

It does not have to be only a physical object right in your hand.

A rough guide is:

• Đây — like day, but with the correct Vietnamese vowel quality
• là — like lah, with a falling tone
• tiền — roughly tee-ən / tee-en
• tiết kiệm — roughly tee-et kee-əm
• của — roughly koo-uh / kuh-uh
• tôi — roughly toy

The full sentence:

• Đây là tiền tiết kiệm của tôi.

A few pronunciation notes:

• đ is pronounced like English d
• tone marks matter a lot
• tiết and kiệm each have their own tones, so try to learn them as whole syllables rather than sounding them out like English

If you want, I can also break the whole sentence down syllable by syllable with tone descriptions.