אם תירשמי היום, אני גם אירשם מחר, כי אני חושבת שיש שם אנשים נחמדים.

Because Hebrew verbs change form to show person, number, and sometimes gender.

Here: תירשמי = you will sign up (addressing one female) אירשם = I will sign up

In the future tense, Hebrew usually marks the subject on the verb itself. So unlike English, you do not need a separate word like will.

The ending -י here marks second person feminine singular in the future tense.

So: תירשמי = you (feminine singular) will sign up

If you were talking to a man, it would be: תירשם = you (masculine singular) will sign up

This -י ending is very common in future forms addressed to one woman, for example: תכתבי = you (f.s.) will write תלמדי = you (f.s.) will study

In Hebrew, a real or possible condition is often expressed with אם + future.

So: אם תירשמי היום literally uses the future: if you will sign up today

But in natural English, we usually say: if you sign up today

That is a normal difference between the two languages. Hebrew commonly keeps the verb in the future after אם in this kind of sentence.

There is no separate word for will here, because Hebrew usually builds the future meaning into the verb itself.

For example: אירשם = I will sign up תירשמי = you will sign up

So the future is carried by the verb form, not by an extra helping word.

להירשם usually means to sign up, to register, or to enroll, depending on context.

In this sentence, sign up or register is the most natural translation.

It is related to the root ר-ש-מ, which has to do with writing down or registering. The form להירשם often has a kind of register oneself / get registered sense, not register something else.

Because the speaker is female.

In Hebrew, the present-tense form here agrees with the speaker’s gender: אני חושבת = I think (said by a woman) אני חושב = I think (said by a man)

So this sentence is being said by a female speaker.

They do two different jobs.

כי means because. It introduces the reason: כי אני חושבת... = because I think...

Then ש- means that: שיש = that there is / that there are

So the structure is: because + I think + that there are...

Literally, the second half is: because I think that there are nice people there

יש means there is or there are. שם means there.

So: יש שם אנשים נחמדים = there are nice people there

A very literal breakdown would be: there-are there nice people

English uses a dummy there in there are. Hebrew does not need that kind of dummy subject; יש already does the existential job.

Here it means people.

Although איש means man, the plural אנשים is very often used in modern Hebrew to mean people in general, not only males.

So: אנשים נחמדים = nice people

That is a very common everyday use of אנשים.

Because אנשים is grammatically masculine plural, so the adjective must agree with it: נחמדים = masculine plural נחמדות = feminine plural

Also, masculine plural is commonly used for mixed groups or unspecified groups in Hebrew.

If you were specifically talking about women, you would say: נשים נחמדות = nice women

גם means also or too.

In: אני גם אירשם מחר the meaning is: I will also sign up tomorrow or I too will sign up tomorrow

Its position helps show what is being added. Here the idea is that the speaker is adding herself to the action. If גם were moved, the emphasis could shift.

If you were talking to a man, you would change תירשמי to תירשם:

אם תירשם היום, אני גם אירשם מחר, כי אני חושבת שיש שם אנשים נחמדים.

If the speaker were a man, you would change חושבת to חושב:

אם תירשמי היום, אני גם אירשם מחר, כי אני חושב שיש שם אנשים נחמדים.

If both were male, both changes would happen:

אם תירשם היום, אני גם אירשם מחר, כי אני חושב שיש שם אנשים נחמדים.