"Shirimasu" (know) is never used.

First of all, I want to make sure you know something: “I know” is not “shirimasu”!

I know. ：shitteimasu

I knew.：shitteimashita

Do you know? ：shitteimasu ka

I don’t know. ：shirimasen

I didn’t know. ：shirimasen deshita

Te-form is used for affirmative sentences and in questions, and masu-form is used for negative sentences. Why is that? First, I would like you to understand the difference between te-form and masu-form.

Te-form

1. indicates an action in progress [example] ima watashi wa asagohan o tabeteimasu. (I am having breakfast now.)

2. indicates the continuation of the state that has happened some time ago. [example] watashi wa Tokyo ni sundeimasu. (I live in Tokyo.)

3. indicates a habitual action [example] maihichi watashi wa 6:00 ni okiteimasu. (I get up at 6 every morning.)

Masu-form

1. indicates a future action [example] ashita watashi wa kaimono ni ikimasu. (I will go shopping tomorrow.)

2. indicates a habitual action [example] mainichi watashi wa 6:00 ni okimasu. (I get up at 6 every morning.) 

3. indicates an general action or fact [example] nihon de gakko wa 4gatsu ni hajimarimasu. (A school year starts in April in Japan.)

Let’s go back to “shiru”, then. The English definition of “know” is as follows:

to have something in one’s mind or memory as a result of experience or learning or information

This means that the state of “I know” has been continuing since someone came to know something sometime in the past. Te-form #2 applies here.

The example I mentioned for te-form #2, “Tokyo ni sundeimasu”, would be translated as “I live in Tokyo” in English. Because this describes the current state starting from the past, we use te-form. If you say, “Tokyo ni sumimasu”, it would be something that is going to happen in the future (masu-form #1).

The next point is the difference between “shiru” and “wakaru”.

I think many of you have already noticed that Japanese use “wakarimasen” instead of “shirimasen” when they say “I don’t know.” For example:

Q. Kono hen ni yubinkyoku ga arimas ka? (Is there any post office around here?)

A. Sumimasen, wakarimasen. (Sorry, I don’t know.)

In this case, “wakarimasen” doesn’t mean “I don’t understand your question”. It means “I don’t know where it is”. Japanese often use “wakaru” in this way, so you must figure out what it is meant from the context.