Ending a sentence with です (desu) makes a sentence sound polite in Japanese. 
The table below shows how to end a sentence in present, past, and negative tenses in plain and polite versions.

For examples. let’s assume that we are finding for someone, or finding a person who did something…

ではありません

Some language teachers teach negation in Japanese by starting with ではありません (dewa arimasen), instead of じゃないです (ja nai desu). You can consider them interchangeable. In order to understand the difference between these two words, we will first see the differences between じゃ and では, and ない and ありません.

じゃ vs では

We can consider じゃ (ja) as an informal / speaking language, while では (dewa) as is a formal / writing language.
E.g., これじゃない (kore ja nai) = これではない (kore dewa nai) = Not this one

ない vs ありません

There is a verb ない (nai), which means “not exist.” ありません (arimasen) is the polite form of this verb, and therefore, これじゃありません (kore ja arimasen) is more polite than これじゃない (kore ja nai).

However, since a negative word ending with ない can be treated as い-adjective in Japanese. We can add です to end a sentence politely. Therefore, ないです (nai desu) is polite enough, yet less formal, to replace ありません.

E.g., これじゃないです (kore ja nai desu) = これではありません (kore dewa arimasen) = not this one

ある vs あります

The opposite of ない (nai) is ある (aru), which means “exist”. The polite form of ある is あります (arimasu).

The table below shows an alternative of the first table. However, this table shows formal ways of writing and speaking, which are not commonly used. です (desu) is replaced by である (de aru) in formal article writing.

で

By looking into the previous table, you may realize that all of them start with で (de). で is a particle in Japanese. Each で is are followed by a verb, and actually, we can also view です and でした as で+す and で+した, where す and した are commonly-seen endings of verbs.

Here, you may question whether we can use other verbs to end a sentence.
The answer is YES, see the following examples

• これでございます (kore de gozaimasu) = This one, sir.
  ** でございます is a humble version of です. It is more polite and commonly used by service providers toward their customers
• これでござる (kore de gozaru) = This one. 
  ** でござる  was used by Samurais in the past (not used nowadays). ござる is a plain form of でございます.
• お車でいらっしゃいますか？ (O kuruma de irasshaimasu ka?) = Is it your car, sir?
  ** でいらっしゃいます is a honorific version of です.   It is used to show respect to the subject being discussed, e.g., a staff asks a customer whether a car is belong to the customer (he has to respect the car).